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 ?