Mean Value Theorem for Continuous Functions

Key Questions

• How do I find the numbers #c# that satisfy the Mean Value Theorem for #f(x)=x^3+x-1# on the interval #[0,3]# ?

  The value of #c# is #sqrt{3}#.

  Let us look at some details.

  M.V.Thm. states that there exists #c# in (0,3) such that

  #f'(c)={f(3)-f(0)}/{3-0}#.

  Let us find such #c#.

  The left-hand side is

  #f'(c)=3c^2+1#.

  The right-hand side is

  #{f(3)-f(0)}/{3-0}={29-(-1)}/{3}=10#.

  By setting them equal to each other,

  #3c^2+1=10 Rightarrow 3x^2=9 Rightarrow x^2=3 Rightarrow x=pm sqrt{3}#

  Since #0<c<3#, #c=sqrt{3}#.

  I hope that this was helpful.

  Wataru · 8 · Sep 28 2014
• What is Rolle's Theorem for continuous functions?

  Actually, Rolle's Theorem require differentiablity, and it is a special case of Mean Value Theorem.
  Please watch this video for more details.
  

  Wataru · · Aug 28 2014
• What is the Mean Value Theorem for continuous functions?

  Mean Value Theorem
  If a function #f# is continuous on #[a,b]# and differentiable on #(a,b)#,
  then there exists c in #(a,b)# such that #f'(c)={f(b)-f(a)}/{b-a}#.

  Wataru · · Sep 7 2014

• What is the Mean Value Theorem for continuous functions?
• What is Rolle's Theorem for continuous functions?
• How do I find the numbers #c# that satisfy the Mean Value Theorem for #f(x)=3x^2+2x+5# on the interval #[-1,1]# ?
• How do I find the numbers #c# that satisfy the Mean Value Theorem for #f(x)=x^3+x-1# on the interval #[0,3]# ?
• How do I find the numbers #c# that satisfy the Mean Value Theorem for #f(x)=e^(-2x)# on the interval #[0,3]# ?
• How do I find the numbers #c# that satisfy the Mean Value Theorem for #f(x)=x/(x+2)# on the interval #[1,4]# ?
• How do I use the Mean Value Theorem to so #4x^5+x^3+2x+1=0# has exactly one real root?
• How do I use the Mean Value Theorem to so #2x-1-sin(x)=0# has exactly one real root?
• How do I find the numbers #c# that satisfy Rolle's Theorem for #f(x)=sqrt(x)-x/3# on the interval #[0,9]# ?
• How do I find the numbers #c# that satisfy Rolle's Theorem for #f(x)=cos(2x)# on the interval #[pi/8,(7pi)/8]# ?
• How do you give a value of c that satisfies the conclusion of the Mean Value Theorem for Derivatives for the function #f(x)=-2x^2-x+2# on the interval [1,3]?
• How do you use the mean value theorem for #2sinx +sin2x# on closed interval of #[4pi, 5pi]#?
• What is the purpose of mean value theorem?
• How do you use the mean value theorem to find roots?
• How do you use the mean value theorem to prove that #sinx-siny = x-y#?
• How do you use the Mean Value Theorem to prove Bernoulli's inequality?
• How do you find the values of c that satisfy the mean value theorem for integrals?
• How do you find the value of c guaranteed by the mean value theorem for integrals #2sec^2x#?
• How do you determine whether the mean value theorem applies to #f(x)=3x-x^2#?
• How do you use the Mean Value Theorem to estimate f(6)−f(2) if suppose f(x) is continuous on [2,6] and −4≤f′(x)≤4 for all x in (2,6)?
• How do you determine whether #f(x) = sqrt( 2x + 3 ) -1# satisfies the hypotheses of the Mean Value Theorem on the interval [3,11] and find all value(s) of c that satisfy the conclusion of the theorem?
• If #f(x)= abs((x^2-12)(x^2+4))#, how many numbers in the interval #-2<=x<=3# satisfy the conclusion of the Mean Value Theorem?
• How do you find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function #f(x)= 6 cos x# on the interval# [-pi/2, pi/2]#?
• How do you verify that the hypotheses of the Mean-Value Theorem are satisfied on the interval [-3,0] and then find all values of c in this interval that satisfy the conclusion of the theorem for # f(x) = 1/(x-1)#?
• How do you find the value of c guaranteed by the mean value theorem if it can be applied for #f(x) = x^2 + 4x + 2# on the interval [-3,-2]?
• How do you find all values of c that satisfy the mean value theorem for #f(x) = x^2# on the interval [-1,1]?
• How do you find the number c that satisfies the conclusion of the Mean Value Theorem for the function #f(x)=x/(x+9)# on the interval [1,4]?
• How do you find the value of c guaranteed by the mean value theorem if it can be applied for #f(x)=x^(1/3)# in the interval [-5,4]?
• How do you give the value of C guaranteed by the mean value theorem for integrals for the function #f(x)=1/sqrt(x+2)# on the interval [-1,23]?
• How do you determine all values of c that satisfy the mean value theorem on the interval [1,3] for # f(x)= ln x^2#?
• How do you verify that the function #f(x)=x/(x+6)# satisfies the hypotheses of The Mean Value Theorem on the given interval [0,1] and then find the number c that satisfy the conclusion of The Mean Value Theorem?
• How do you verify that the hypothesis of the Mean Value Theorem are satisfied for #f(x)=sqrt(25-x^2)#?
• Can the mean value theorem be applied to #f(x) = 2(sqrt x) + x# on the interval [1,4]?
• How do you find all numbers c that satisfy the conclusion of the mean value theorem for #f(x) = sqrt(1-x^2)# on the interval [0-1]?
• How do you verify that the function #f(x) = (x)/(x+2)# satisfies the hypotheses of the Mean Value Theorem on the given interval [1,4], then find all numbers c that satisfy the conclusion of the Mean Value Theorem?
• How do you find a number c that satisfies the conclusion of the theorem for the function #f(x) = x^2 - 3x + 1# on the interval [-1,1]?
• What is the difference between Mean value theorem, Average value and Intermediate value theorem?
• How do you verify that the hypothesis of the Mean-Value Theorem are satisfied on the interval [2,5], and find all values of c in the given interval that satisfy the conclusion of the theorem for #f(x) = 1 / (x-1)#?
• Does the function #f(x) = ln x# satisfy the hypotheses of the Mean Value Theorem on the given interval [1, 7]?
• Using the principle of the mean-value theorem on the indicated interval, how do you find all numbers c that satisfy the conclusion of the theorem for #f(x) = 5(1 + 2x)^(1/2)# in the interval [1,4]?
• How do you determine if the function #sqrt (x(1-x))# defined on the interval [0,1] satisfies the hypotheses of the Mean Value Theorem, and then find the value or values that satisfy the equation #(f(b)-f(a))/(b-a)=f'(c)#?
• How do you find all numbers c in the interval show that the function #f(x)=x^3+x+1# satisfies the mean value theorem on the interval [-1,2]?
• Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval if #f(x) = 2x^2 − 3x + 1# and [0, 2]?
• How do you find all values of c that satisfy the Mean Value Theorem for integrals for #f(x)=x^4# on the interval [-4,4]?
• How do you find the values of C guaranteed by the Mean Value Theorem for #f(x)= 9/x^3# over [1, 3]?
• How do you determine whether the Mean Value Theorem can be applied to #f(x) = sqrt (x-7)# on the interval [11,23]?
• How do you use the Mean Value Theorem to solve #f(x)=x - sqrtx# on the closed interval [0,4]?
• Let f be given by the function #abs(x^2-4x)# from [-1,1], how do you find all values of c that satisfy the Mean Value Theorem?
• How do you find the value of values of c that satisfy the equation [f(b)-f(a)]/(b-a) in the conclusion of the Mean Value Theorem for the function #f(x)=x^2+2x+2# on the interval [-2,1]?
• How do you check the hypotheses of Rolles Theorem and the Mean Value Theorem and find a value of c that makes the appropriate conclusion true for #f(x) = x^3+x^2#?
• How many values of c satisfy the conclusion of the Mean Value Theorem for f(x) = x^3 + 1 on the interval [-1,1]?
• How do you verify that #y = x^3 + x - 1# over [0,2] satisfies the hypotheses of the Mean Value Theorem?
• By the Mean Value Theorem, we know there exists a c in the open interval (2,4) such that f′(c) is equal to this mean slope, how do you find the value of c in the interval which works for #f(x)=−3x^3−4x^2−3x+3#?
• How do youfFind the value of c guaranteed by the mean value theorem for integrals #f(x) = - 4 / x^2# on the interval [ 1, 4 ]?
• How do you find all numbers c that satisfy the conclusion of the Mean Value Theorem for #f(x)= x^3 + x - 1# over [0,2]?
• How do you determine whether the function #f(x) = abs(x-3)# satisfies the hypotheses of the mean value theorem on the indicated interval (a,b), and if so how do you find all numbers c on [0,4] ?
• How do you verify that the function #f(x)=x^(3)-x^(2)-12x+4# satisfies the three hypotheses of Rolle's Theorem on the given interval [0,4] and then find all numbers c that satisfy the conclusion of Rolle's Theorem?
• How do you show that #f(x)=6x^2 - 24x + 22# satisfies the hypotheses of Rolle's theorem on [0,4]?
• How to use rolles theorem for #f(x)= (x^3/3)- 3x# on the interval [-3,3]?
• How do you find the number c that satisfies the conclusion of Rolle's Theorem #f(x) = x^3 - x^2 - 20x + 3# on interval [0, 5]?
• How do you know whether Rolle's Theorem applies for #f(x)=x^2/3+1# on the interval [-1,1]?
• How do you verify that the function #f(x)= (sqrt x)- 1/3 x# satisfies the three hypothesis of Rolles's Theorem on the given interval [0,9] and then find all numbers (c) that satisfy the conclusion of Rolle's Theorem?
• How do you verify that the hypotheses of rolles theorem are right for #f(x)= x sqrt(x+2)# over the interval [2,4]?
• How do you know why Rolle's Theorem does not apply to #f(x)= x^(2/3)# on the interval [-1,1]?
• How do you determine if Rolle's Theorem can be applied to the given functions #f(x) = x^4 -2x^2# on interval [-2,2]?
• How do you find the number c that satisfies the conclusion of Rolle's Theorem for #f(x) = cos(5x)# for [π/20,7π/20]?
• How do you verify that the function #f(x)= sin(22pix)# satisfies the three hypotheses of Rolle's Theorem on the given interval [-1/11, 1/11] and then find all numbers c that satisfy the conclusion of Rolle's Theorem?
• How do you verify that the function #f(x)=x^3 - 21x^2 + 80x + 2# satisfies Rolle's Theorem on the given interval [0,16] and then find all numbers c that satisfy the conclusion of Rolle's Theorem?
• How do you determine whether Rolle's theorem can be applied to #f(x) = (x^2 - 1) / x# on the closed interval [-1,1]?
• How do you determine whether Rolle’s Theorem can be applied to #f(x)=x(x-6)^2# on the interval [0,6]?
• Does rolle's theorem apply for #f(x) = abs(x-2)# on [0,4]?
• How do you determine whether rolles theorem can be applied to #f(X)=(x^2-2x-3)/(x+2)# on the closed interval [-1,3] and if it can find all value of c such that f '(c)=0?
• How do you determine if rolles theorem can be applied to #f(x)=x^2-3x+2# on the interval [1, 2] and if so how do you find all the values of c in the interval for which f'(c)=0?
• How do you determine if rolles theorem can be applied to #f(x)= 3sin(2x)# on the interval [0, 2pi] and if so how do you find all the values of c in the interval for which f'(c)=0?
• Is Rolle's theorem applicable to #f(x)=tanx#, when 0 < x < r??
• How do you determine if rolles theorem can be applied to #f(x) = 2x^3 - x^2 - 8x + 4# on the interval [-2,2] and if so how do you find all the values of c in the interval for which f'(c)=0?
• How do you determine if rolles theorem can be applied to #sqrt(x) - 1/5x # on the interval [0,25] and if so how do you find all the values of c in the interval for which f'(c)=0?
• How do you determine if rolles theorem can be applied to #f(x) = 2 − 20x + 2x^2# on the interval [4,6] and if so how do you find all the values of c in the interval for which f'(c)=0?
• How do you determine if rolles theorem can be applied to #f(x)= 10 sin (2x)# on the interval [0,2pi] and if so how do you find all the values of c in the interval for which f'(c)=0?
• How do you determine if rolles theorem can be applied to #f(x) = 2x^2 − 5x + 1# on the interval [0,2] and if so how do you find all the values of c in the interval for which f'(c)=0?
• How do you determine if rolles theorem can be applied to # f(x) = sin 2x# on the interval [0, (pi/2)] and if so how do you find all the values of c in the interval for which f'(c)=0?
• How do you determine if rolles theorem can be applied to #f(x)=xsinx# on the interval [-4,4] and if so how do you find all the values of c in the interval for which f'(c)=0?
• How do you determine if rolles theorem can be applied to #f(x) = x^3 - x^2- 20x + 7 # on the interval [0,5] and if so how do you find all the values of c in the interval for which f'(c)=0?
• If f is continuous on [0,2] with f(0) = f(2), show that there is a c element of [0,2] such that f(c) = f(c+1)?
• How do you show that #1 + 2x +x^3 + 4x^5 = 0# has exactly one real root?
• What is the difference between rolle's theorem and mean value theorem?
• Does the function #f(x) = 2x^2 − 5x + 1# satisfy the hypotheses of the Mean Value Theorem on the given interval [0,2]?
• What is the average or mean slope of the function #2x^3 - 6x^2 - 48x + 4# on the interval [-4,9]?
• How do you find the value of c guaranteed by the Mean Value Theorem for #f(x)=(2x)/(x^2+1)# on the interval [0,1]?
• How do you find the number c that satisfies the conclusion of the Mean Value Theorem for #f( x) = e^(-2x)# on [0,3]?
• How do you use the Intermediate Value Theorem to show that the polynomial function #f(x) = x^3 + 2x - 1# has a zero in the interval [0,1]?
• How do you use the Intermediate Value Theorem to show that the polynomial function #sin x + cos x - x = 0# has a real solution?
• How do you use the Intermediate Value Theorem to show that the polynomial function #x^3-3x+4.1=0# has a root on the interval (0,1)?
• How do you use the Intermediate Value Theorem to show that the polynomial function # [cos (t)] t^3 + 6sin^5(t) -3=0# has a root on the interval (0,2pi)?
• How do you use the Intermediate Value Theorem to show that the polynomial function #f(x) = x^3 -3x^2 + 3# has one zero?
• How do you use the Intermediate Value Theorem to show that the polynomial function #f(x) = x^4 -10x^2 + 3# has one zero?
• How do you use the Intermediate Value Theorem to show that the polynomial function #f(x)=3x-2sin(x)+7# has one zero?
• How do you use the Intermediate Value Theorem to show that the polynomial function #f(x) = x^5 - 3x^4 - 2x^3 + 6x^2 + x + 2# has a zero in the interval [1.7, 1.8]?
• How do you use the Intermediate Value Theorem to show that the polynomial function #f(x) = x^3 − 4x^2 − 2# has a zero in the interval [0, 1]?
• How do you use the Intermediate Value Theorem to show that the polynomial function #f(x) = x^4 + 8x^3 - x^2 + 2# has a zero in the interval [-1, 1]?
• How do you use the Intermediate Value Theorem to show that the polynomial function #P(x) = x^3 - 3x^2 + 2x - 5# has a zero in the interval [2, 3]?
• How do you use the Intermediate Value Theorem to show that the polynomial function #P(x) = x^4 + 2x^3 + 2x^2 - 5x + 3# has a zero in the interval [0, 1]?
• How do you use the Intermediate Value Theorem to show that the polynomial function #P(x) = x^3 - 2x^2 - 5# has a zero in the interval [-1, -2]?
• How do you use the Intermediate Value Theorem to show that the polynomial function #x^3 - 2x^2 + 3x = 5# has a zero in the interval [1, 2]?
• How do you use the Intermediate Value Theorem to show that the polynomial function #sin2x + cos2x - 2x = 0# has a zero in the interval [0, pi/2]?
• How do you use the Intermediate Value Theorem to show that the polynomial function # 2tanx - x - 1 = 0# has a zero in the interval [0, pi/4]?
• How do you use the Intermediate Value Theorem to show that the polynomial function # f(x)= x^3-5x-3# has three roots in the interval [-3, 3]?
• How do you use the Intermediate Value Theorem to show that the polynomial function # 2x^3 + x^2 +2# has a root in the interval [-2, -1]?
• How do you use the Intermediate Value Theorem to show that the polynomial function # f(x) = (x^3)/2 - 4x + 1/(x)# has a root in the interval [-3, -1]?
• How do you use the Intermediate Value Theorem to show that the polynomial function #f(x) = -1 + 3 cos x# has a root in the interval [0, 5pi/2]?
• How do you use the Intermediate Value Theorem to show that the polynomial function # f(x) = x^2 − x + 1# has a root in the interval [-1, 6]?
• How do you use the Intermediate Value Theorem to show that the polynomial function # x^3+2x^2-42# has a root in the interval [0, 3]?
• How do you use the Intermediate Value Theorem to show that the polynomial function #F(x)=x^3+2x+1 # has a root in the interval [-2, 1]?
• How do you use the Intermediate Value Theorem to show that the polynomial function #f(x) = 10x^4 - 2x^2 + 7x - 1# has a root in the interval [-3, 0]?
• Question #4f1cd
• Question #cd78d
• Question #d2272
• Question #3acdb
• How do you determine all values of c that satisfy the mean value theorem on the interval [0,1] for # sqrt (x(1-x))#?
• How do you determine all values of c that satisfy the conclusion of the mean value theorem on the interval [1, 18] for #f(x)=x/(x+9)#?
• How do you determine all values of c that satisfy the mean value theorem on the interval [3,6] for #f(x)=(x-4)^2-1#?
• How do you determine all values of c that satisfy the mean value theorem on the interval [2,5] for #f(x) = 1 / (x-1)#?
• How do you determine all values of c that satisfy the conclusion of the mean value theorem on the interval [-pi/2, pi/2] for #f(x)=x-cosx#?
• How do you determine all values of c that satisfy the conclusion of the mean value theorem on the interval [0,1] for #f(x) = (x)arcsin(x)#?
• How do you determine all values of c that satisfy the mean value theorem on the interval [6,10] for #f(x)= ln (x-5)#?
• How do you determine all values of c that satisfy the conclusion of the mean value theorem on the interval [-1, 23] for #f(x)=1/sqrt(x+2)#?
• How do you determine all values of c that satisfy the conclusion of the mean value theorem on the interval [1,4] for #f(x)=x/(x+9)#?
• How do you determine all values of c that satisfy the mean value theorem on the interval [-3,-2] for #f(x) = x^2 + 4x + 2#?
• How do you determine all values of c that satisfy the conclusion of the mean value theorem on the interval [0, pi] for #f(x)=2sin(x)+sin(4x) #?
• How do you determine all values of c that satisfy the mean value theorem on the interval [-1,1] for #(x^2 − 9)(x^2 + 1)#?
• How do you determine all values of c that satisfy the conclusion of the mean value theorem on the interval [0,2] for #f(x) = 2x^2 − 5x + 1#?
• How do you determine all values of c that satisfy the conclusion of the mean value theorem on the interval [-1,1] for #f(x) = x(x^2 - x - 2)#?
• How do you determine all values of c that satisfy the conclusion of the mean value theorem on the interval [0,7] for #f(x)=1/((x+1)^6)#?
• How do you determine all values of c that satisfy the mean value theorem on the interval [0,1] for #f(x)= x/(x+6)#?
• How do you determine all values of c that satisfy the mean value theorem on the interval [-6, 7] for #f(x)=2x^3–9x^2–108x+2#?
• How do you determine all values of c that satisfy the mean value theorem on the interval [1,2] for # f(x) = ln(x)#?
• How do you determine all values of c that satisfy the mean value theorem on the interval [-1,1] for #f(x) = 3x^5+5x^3+15x #?
• How do you determine all values of c that satisfy the mean value theorem on the interval [1, 1.5] for #f(x)=sinx#?
• How do you determine all values of c that satisfy the mean value theorem on the interval [1, 4] for #f(x)=1/sqrt(x)#?
• How do you determine all values of c that satisfy the conclusion of the mean value theorem on the interval [3, 5] for #f(x)=2sqrt(x)+3#?
• How do you determine all values of c that satisfy the mean value theorem on the interval [1,9] for #f(x)=x^-4#?
• How do you determine all values of c that satisfy the mean value theorem on the interval [0,3] for #f(x) = x^3 + x - 1 #?
• How do you determine all values of c that satisfy the mean value theorem on the interval [pi/2, 3pi/2] for # f(x) = sin(x/2)#?
• How do you determine all values of c that satisfy the mean value theorem on the interval [-1, 1] for #f(x)=3sin(2πx)#?
• How do you determine all values of c that satisfy the conclusion of the mean value theorem on the interval [11, 23] for #f(x) = sqrt (x-7)#?
• How do you determine all values of c that satisfy the conclusion of the mean value theorem on the interval [0, 8] for #f(x) = x^3 + x - 1#?
• How do you determine all values of c that satisfy the mean value theorem on the interval [0, 2] for #y = x^3 + x - 1#?
• How do we find whether the function #f(x)=cosx-x^2# has a root between #x=pi/4# and #x=pi/3# or not?
• Using the principle of the mean-value theorem on the indicated interval, how do you find all numbers c that satisfy the conclusion of the theorem #f(x) = 1 / (x-1)#; [2, 5]?
• Using the principle of the mean-value theorem on the indicated interval, how do you find all numbers c that satisfy the conclusion of the theorem #f(x)=x-cosx#; [-pi/2, pi/2]?
• Using the principle of the mean-value theorem on the indicated interval, how do you find all numbers c that satisfy the conclusion of the theorem #f(x) = x³ + 5x² - 2x - 5#; [-1, 2]?
• Using the principle of the mean-value theorem on the indicated interval, how do you find all numbers c that satisfy the conclusion of the theorem #f(x)= 6 cos (x)#; [-pi/2, pi/2]?
• Using the principle of the mean-value theorem on the indicated interval, how do you find all numbers c that satisfy the conclusion of the theorem #f(x) = 1/(x-1)#; [-3, 0]?
• Using the principle of the mean-value theorem on the indicated interval, how do you find all numbers c that satisfy the conclusion of the theorem #f(x) = ln (x-1)#; [2, 6]?
• Using the principle of the mean-value theorem on the indicated interval, how do you find all numbers c that satisfy the conclusion of the theorem #f(x)=x^3-2x^2#; [0, 2]?
• How do you find the number c that satisfies the conclusion of the Mean Value Theorem for the function #f(x)=x^3 - 2x + 1# on the interval [0,2]?
• How do you find the number c that satisfies the conclusion of the Mean Value Theorem for the function #f(x) = x^2 + 4x + 2# on the interval [-3,-2]?
• How do you find the number c that satisfies the conclusion of the Mean Value Theorem for the function #f(x)=x-2sinx# on the interval [0, pi]?
• How do you find the number c that satisfies the conclusion of the Mean Value Theorem for the function #f(x)=x^2 - 2x + 5# on the interval #[1, 3]#?
• How do you find the number c that satisfies the conclusion of the Mean Value Theorem for the function #f(x) = x^3 + x^2# on the interval [0,1]?
• How do you find the number c that satisfies the conclusion of the Mean Value Theorem for the function #f(x) = ln x# on the interval [1,7]?
• Use limits to verify that the function #y=(x-3)/(x^2-x)#has a vertical asymptote at #x=0#? Want to verify that #lim_(x ->0)((x-3)/(x^2-x))=infty#?
• Question #a16fd
• How do you determine if Rolles Theorem applies to the given function #x^3 - 9x# on [0,3]. If so, how do you find all numbers c on the interval that satisfy the theorem?
• How do you use the mean value theorem to explain why (-1) is the only zero of the function f(x)=x³+3x²+9x+7?
• Round 25 to the nearest percent?
• In the following graph, how do you determine the value of c such that #lim_(x->c) f(x)# exists?
• In the first Mean Value Theorem #f(b)=f(a)+(b-a)f'(c), a<c<b, f(x) =log_2 x, a=1 and f'(c)=1. How do you find b and c?
• Given the function #f(x)=((x)/(x+4)) #, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [1,8]?
• Given the function #f(x) = - 4 / x^2#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [1,4] and find the c?
• Given the function #f(x) = x^2#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-1,1] and find the c?
• Given the function #f(x) = 2x^2 − 3x + 1#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [0,2] and find the c?
• Given the function #f(x)=x-cosx#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-pi/2,pi/2] and find the c?
• Given the function #f(x) = absx#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-4,6] and find the c?
• Given the function #f(x) = x^(1/3) #, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-5,4] and find the c?
• Given the function #f(x)=x^2 - 2x + 5#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [1,3] and find the c?
• Given the function #f(x) = x^(2/3)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-1,8] and find the c?
• Given the function # f(x)=3x^3−2x#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-4,4] and find the c?
• Given the function # f(x) = 9/x^3#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [1,3] and find the c?
• Given the function #f(x) = 1 / (x-1)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [2,5] and find the c?
• Given the function #f(x)= abs((x^2-12)(x^2+4))#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-2,3] and find the c?
• Given the function #f(x) = 5(1 + 2x)^(1/2)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [0,4] and find the c?
• Given the function # f(x)=1/sqrt(x+2)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-1,23] and find the c?
• Given the function # f(x)=1/sqrt(x+2)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-1,23] and find the c?
• Given the function #f(x)=x^3-9x#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-1,1] and find the c?
• Given the function #f(x) = 4 x #, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [4,9] and find the c?
• Given the function #f(x) = x² - 3x + 1#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-1,1] and find the c?
• Given the function #f(x)= 6 cos (x) #, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-pi/2, pi/2] and find the c?
• Given the function #f(x) = x^3 + x - 1#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [0,4] and find the c?
• Given the function #f(x)=x/(x+9)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [1,4] and find the c?
• Given the function #f(x)=x/(x+9)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [1,18] and find the c?
• Given the function #f(x)= ln x^2#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [1,3] and find the c?
• Given the function # f(x) = 8 sqrt{ x} + 1#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [1,10] and find the c?
• Given the function #f(x)=(x-4)^2-1#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [3,0] and find the c?
• Given the function #f(x)=abs(x-3)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [0,4] and find the c?
• Given the function #f(x)=x/(x+6)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [0,1] and find the c?
• Given the function #f(x) = (x)/(x+2)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [1,4] and find the c?
• Given the function #f(x)=5sqrt(25-x^2)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [0,5] and find the c?
• Given the function #f(x)=-x^2+8x-17#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [3,6] and find the c?
• Given the function #f(x)=x^3-9x^2+24x-18#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [2,4] and find the c?
• Given the function #f(x)=x^3+3x^2-2#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-2,0] and find the c?
• Given the function #f(x)=x^2/2-2x-1#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-1,1] and find the c?
• Given the function #f(x)=-x^3+4x^2-3#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [0,4] and find the c?
• Given the function #f(x)=(x^2-9)/(3x)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [1,4] and find the c?
• Given the function #f(x)=-(-2x+6)^(1/2)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-2,3] and find the c?
• Given the function #f(x)=-(-5x+25)^(1/2_#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [3,5] and find the c?
• Given the function #f(x)==x^2/(4x+8)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-3,-1] and find the c?
• Given the function #f(x)=(-x^2+9)/(4x)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [1,3] and find the c?
• Given the function #f(x)=-(6x+24)^(2/3)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-4,-1] and find the c?
• Given the function #f(x)=(x-3)^(2/3)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [1,4] and find the c?
• Given the function #f(x)=5-4/x#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [1,4] and find the c in the conclusion?
• Given the function #f(x)=sqrt(2-x)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-7,2] and find the c?
• Given the function #f(x)=(x^2-1)/(x-2)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-1,3] and find the c?
• Given the function #f(x)=(x^2-1)/x#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-1,1] and find the c?
• Given the function #f(x)=sinx#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [0, pi] and find the c?
• Given the function #f(x)=(x+1)/x#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [1/2, 2] and find the c?
• Given the function #f(x)=abs(x-3)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [0,6] and find the c?
• Given the function #f(x)=x(x^2-x-2)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-1,1] and find the c?
• Given the function #f(x)=x^(2/3)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [0,1] and find the c?
• Question #88f84
• Does the formula #f(x) = sqrt(x)# define a function ?
• How do you use the intermediate value theorem to show that there is a root of the equation #2x^3+x^2+2=0# over the interval (-2, -1)?
• How do you use the intermediate value theorem to show that there is a root of the equation #e^(-x^2)# over the interval (0,1)?
• Question #be0d7
• Question #bd1e6
• Question #89907
• Let #f# such that #f:RR->RR# and for some positive #a# the equation #f(x+a)=1/2+sqrt(f(x)+f(x)^2)# holds for all #x#. Prove that the function #f(x)# is periodic?
• Question #79fec
• How do you find all numbers c that satisfies the conclusion of the Mean Value Theorem for the function #f(x)=9x^2+6x+4# in the interval [-1,1]?
• Question #82b04
• The function #f(x) = tan(3^x)# has one zero in the interval #[0, 1.4]#. What is the derivative at this point?
• Question #16211
• The Mean Value Theorem applies to the given function on the given interval. How do you find all possible values of #f(x)=x^(9/4)# on the interval [0,1]?
• How do you find the value of c that satisfy the equation #(f(b)-f(a))/(b-a)=f'(c)# in the conclusion of the mean value theorem for the function #f(x)=4x^2+4x-3# on the interval [-1,0]#?
• How do you determine whether the function satisfies the hypotheses of the Mean Value Theorem for #f(x)=x^(1/3)# on the interval [-5,4]?
• How do you use Rolle's Theorem on a given function #f(x)#, assuming that #f(x)# is not a polynomial?
• Question #fe61a
• Using mean value theorem show that: #x< sin^-1x#, for #x>0#?
• Question #6e833
• Question #38830
• Question #1ba37
• #x^3+24x-16# [0,4] verify mean value theorem?
• Find value(s) c ∈ (−2, 4) such that f'(c) is parallel to the chord line joining ?