Identifying Turning Points (Local Extrema) for a Function

Key Questions

• How do you find the extreme values of the function and where they occur?

  Answer:

  See below.

  Explanation:

  To find extreme values of a function #f#, set #f'(x)=0# and solve. This gives you the x-coordinates of the extreme values/ local maxs and mins.

  For example. consider #f(x)=x^2-6x+5#. To find the minimum value of #f# (we know it's minimum because the parabola opens upward), we set #f'(x)=2x-6=0# Solving, we get #x=3# is the location of the minimum. To find the y-coordinate, we find #f(3)=-4#. Therefore, the extreme minimum of #f# occurs at the point #(3,-4)#.

  Teddy · 1 · Jul 5 2018
• How many turning points can a cubic function have?

  Any polynomial of degree #n# can have a minimum of zero turning points and a maximum of #n-1#. However, this depends on the kind of turning point.

  Sometimes, "turning point" is defined as "local maximum or minimum only". In this case:

  • Polynomials of odd degree have an even number of turning points, with a minimum of 0 and a maximum of #n-1#.
  • Polynomials of even degree have an odd number of turning points, with a minimum of 1 and a maximum of #n-1#.

  However, sometimes "turning point" can have its definition expanded to include "stationary points of inflexion". For an example of a stationary point of inflexion, look at the graph of #y = x^3# - you'll note that at #x = 0# the graph changes from convex to concave, and the derivative at #x = 0# is also 0.

  If we go by the second definition, we need to change our rules slightly and say that:

  • Polynomials of degree 1 have no turning points.
  • Polynomials of odd degree (except for #n = 1#) have a minimum of 1 turning point and a maximum of #n-1#.
  • Polynomials of even degree have a minimum of 1 turning point and a maximum of #n-1#.

  So, in part, it depends on the definition of "turning point", but in general most people will go by the first definition.

  CJ · 8 · Sep 6 2014
• What is special about a turning point?

  For a differentiable function #f(x)#, at its turning points, #f'# becomes zero, and #f'# changes its sign before and after the turning points.

  ---

  I hope that this was helpful.

  Wataru · 1 · Nov 7 2014

• How do you find the x coordinates of the turning points of the function?
• How do you find the turning points of a cubic function?
• How many turning points can a cubic function have?
• How do you find the coordinates of the local extrema of the function?
• How do you find the local extrema of a function?
• How many local extrema can a cubic function have?
• How do I find the maximum and minimum values of the function #f(x) = x - 2 sin (x)# on the interval #[-pi/4, pi/2]#?
• If #f(x)=(x^2+36)/(2x), 1 <=x<=12#, at what point is f(x) at a minimum?
• How do you find the maximum of #f(x) = 2sin(x^2)#?
• How do you find a local minimum of a graph using the first derivative?
• How do you find the absolute minimum and maximum on #[-pi/2,pi/2]# of the function #f(x)=sinx^2#?
• How do you find the minimum values for #f(x)=2x^3-9x+5# for #x>=0#?
• How do you use the second derivative test to find all relative extrema of #f(x)=5+3x^2-x^3#?
• How do you find all relative extrema for #f(x) = 8/(x^2+2)#?
• How do you find all extrema in the interval [0, 2(pi)] for #y= sin x + cos x#?
• Given the function #y=2-x^2#, how do you determine the relative maximum or the relative minimum?
• How do you find absolute extrema of the function #g(x) = 2x + 5cosx# on the interval [0,2pi]?
• How do you find the extrema for #f(x)= (e^(10x))/(1+ e^(10x))# for [-5,5]?
• How do you find all local extrema/ relative maxima and minima for the function #y = x^3 - 3x^2 - 9x +15#?
• How do you find the extrema for #f(x)=x^4-18x^2+7#?
• How do you find the relative extrema for #f(x) =2x- 3x^(2/3) +2# on the interval [-1,3]?
• What is the absolute extrema of the function: #2x/(x^2 +1)# on closed interval [-2,2]?
• Find the absolute extrema of the given function #f(x)= sinx+cosx# on interval #[0,2pi]#?
• How do you find the extrema for #g(x) = sqrt(x^2 + 2x + 5)#?
• How duo you find all extrema in the interval #[0, 2pi]# if #y=x+sin x#?
• How do you find the extrema for #f(x) = x^2 +2x - 4# for [-1,1]?
• What are the absolute extrema of #y=cos^2 x - sin^2 x# on the interval [-2,2]?
• How do you find the coordinates of relative extrema #f(x)=x^3-4x^2+x+6#?
• How do you find all relative extrema of the function #f(x)= -x^3 -6x^2-9x-2#?
• How do you find all the extrema for #f(x) = x/(x^2+x+1)# on [-2,2]?
• How do you find all extrema for #f(x) = 2x + ln x#?
• How do you find the extrema for #f(x) = sec x# on the closed interval #[-pi/6, pi/3]#?
• How do you find the extrema of #f(x)=4 x^3-26 x^2+16x+1# on [0,3]?
• How do you find the relative extrema of the function #f (x) = x^3 + 6 x^2#?
• How do you find all relative extrema and points of inflection for the equation: #y=x^2 log_3x#?
• How do you find the relative extrema of the function #f (x)=x^4+4x^3+4x^2#?
• How do you locate the absolute extrema of the function #f(x)=x^3-12x# on the closed interval [0,4]?
• How would a horizontal line work in the Extreme Value Theorem?
• How do you find the global extreme values for #h(x)= x^2-3x# on [0,2]?
• How do you find the global extreme values for #V(x) = x(10 - 2x)( 16 - 2x)# on [0,5]?
• How do you find the global extreme values for #f(t) = tsqrt(4 - t²)# on [-1,2]?
• How do you find the global extreme values for #f(t) = 2cost + sin2t# on [0,pi/2]?
• How do you find the global extreme values for # y=x^2-6x-1# on [-2,2]?
• How do you find the absolute max and min for #f(x) = 5 + 2x# on [-2,1]?
• How do you find the absolute extrema of the function on the indicated interval by using the concept of the Extreme-Value Theorem f(x) = { |x| if -3 ≤ x ≤ 2 , 4-x if 2 < x ≤ 3 ; [ -3, 3]?
• What is the difference between Intermediate Value Theorem and the Extreme Value Theorem?
• What theorem guarantees the existence of an absolute maximum value and an absolute minimum value for f?
• How do use the first derivative test to determine the local extrema #f(x) = 3(x-4)^(2/3) +6#?
• How do use the first derivative test to determine the local extrema #f(x) = x^3 - x^2 - x + 3#?
• How do use the first derivative test to determine the local extrema #y = (x^2 + 2) /( x^2 + 1)#?
• How do use the first derivative test to determine the local extrema #(x)/[(x^2) +3]#?
• How do use the first derivative test to determine the local extrema #1/(x^2-x+2)#?
• How do use the first derivative test to determine the local extrema #(x^2-10x)^4#?
• How do use the first derivative test to determine the local extrema #x^2/(3(8-x))#?
• How do use the first derivative test to determine the local extrema #f(x)=x^4-4x^3+4x^2+6 #?
• How do use the first derivative test to determine the local extrema #x^2-x-1#?
• How do use the first derivative test to determine the local extrema #y = sin x cos x#?
• How do use the first derivative test to determine the local extrema #f(x)=x-2tan(x)#?
• How do use the first derivative test to determine the local extrema #f(x)= -x^3 + 12x#?
• How do use the first derivative test to determine the local extrema #f(x)= x^3 - x^2 - 40x + 8#?
• How do use the first derivative test to determine the local extrema #f(x)= 4x^3 - 3x^4#?
• How do use the first derivative test to determine the local extrema #3-x^2#?
• How do use the first derivative test to determine the local extrema #x^2+1#?
• How do use the first derivative test to determine the local extrema #f(x) = x / (x^2+1)#?
• How do use the first derivative test to determine the local extrema #x^2-2x-3#?
• How do use the first derivative test to determine the local extrema #f(x) = (x+1)(x-3)^2#?
• How do use the first derivative test to determine the local extrema #f(x) = (x+3)(x-4)^2#?
• How do use the first derivative test to determine the local extrema #f(x) = x^3 + 6x^2#?
• How do use the first derivative test to determine the local extrema #f(x) = x³+3x²-9x+15#?
• How do use the first derivative test to determine the local extrema # f(x) = 3x^4-8x^3-90x^2+50#?
• How do use the first derivative test to determine the local extrema #f(x) = xsqrt(25-x^2)#?
• How do use the first derivative test to determine the local extrema #F(x) = -2x^3 - 9x^2 + 24x + 40#?
• How do use the first derivative test to determine the local extrema #f(x)=x^3-2x +pi #?
• How do use the first derivative test to determine the local extrema #y = x + sinx#?
• How do use the first derivative test to determine the local extrema #f(x)=x^3 - 9x^2 + 27x#?
• How do use the first derivative test to determine the local extrema #36x^2 +24x^2#?
• How do use the first derivative test to determine the local extrema #y=x(sqrt(8-x^2))#?
• How do use the first derivative test to determine the local extrema #f(x) = 3x^5 - 20x^3#?
• How do use the first derivative test to determine the local extrema #y= (x²-3x+3)/ (x-1) #?
• What are the extrema of #f(x)=-sinx-cosx# on the interval #[0,2pi]#?
• What are the extrema of #f(x)=-sin^2(ln(x^2))-cos^2(ln(x^2))# on the interval #[0,2pi]#?
• What are the local extrema of #f(x) = 2 x + 3 /x#?
• What are the local extrema of #f(x) = tan(x)/x^2+2x^3-x#?
• What are the local extrema of #f(x) = cos(x)/x^2+2x^3-x#?
• What are the local extrema of #f(x)= 5x - 3#?
• What are the local extrema of #f(x)= -x^3 + 3x^2 + 10x + 13#?
• What are the local extrema of #f(x)= 4^x# if they exist?
• What are the local extrema of #f(x)= sinx# on #[0,2pi]#?
• If #f'(x) = (x-8)^9 (x-4)^7 (x+3)^7#, what are the local minima and maxima of #f(x)#?
• What are the local maxima and minima of #f(x) = 4x^3 + 3x^2 - 6x + 1#?
• What are the local maxima and minima of #f(x)= (x^2)/(x-2)^2#?
• If you only have #f'(x)# is it possible to differentiate the local and global extrema of #f(x)#?
• What are the extrema and saddle points of #f(x, y) = xy+27/x+27/y#?
• What are the extrema and saddle points of #f(x, y) = x^2 + y^2 xy+27/x+27/y#?
• What are the extrema and saddle points of #f(x, y) = x^2 + y^2+27xy+9x+3y#?
• What are the extrema and saddle points of #f(x,y) = 2x^3 + xy^2 + 5x^2 + y^2#?
• What are the extrema and saddle points of #f(x,y) = 2x^(2) + (xy)^2 + 5x^2 - y/x#?
• What are the extrema of #f(x) = 5 + 9x^2 − 6x^3#?
• What are the extrema of #f(x) = (3x) / (x² - 1)#?
• What are the extrema and saddle points of #f(x,y) = xy + 1/x^3 + 1/y^2#?
• What are the extrema and saddle points of #f(x,y) = x^2y+y^3x -1/x^3 + 1/(xy^2)#?
• What are the extrema and saddle points of #f(x,y) = x^2y-y^2x#?
• What are extrema and saddle points of #f(x,y)=(x+y+1)^2/(x^2+y^2+1)#?
• What are the extrema of #f(x) = e^x(x^2+2x+1)#?
• What are the extrema of #f(x)=2x^3 + 5x^2 - 4x - 3 #?
• What are extrema and saddle points of #f(x, y) = x^3y + 36x^2 - 8y#?
• What are the extrema of #h(x) = 7x^5 - 12x^3 + x#?
• Why is a point, b, an extremum of a function if #f'(b)=0#?
• What are the extrema of #f(x) = 1 - sqrt(x)#?
• What are the extrema of #f(x) = 64-x^2# on the interval #[-8,0]#?
• What are the extrema and saddle points of #f(x, y) = 6 sin x sin y# on the interval #x,y in[-pi,pi]# ?
• What are the extrema and saddle points of #f(x, y) = 6 sin(-x)* sin^2( y)# on the interval #x,y in[-pi,pi]# ?
• What are the extrema of #y=2x^3 - 5x^2 - 4x + 7#?
• What are the extrema of #f(x)=x^3-2x+5 # on #[-2,2]?
• What are the extrema of #f(x) = 2 + (x + 1)^2 # on #[-2,4]?
• What are the extrema of #f(x) = 7e^x#?
• What are the extrema and saddle points of #f(x, y) = xye^(-x^2-y^2)#?
• What are the extrema and saddle points of #f(x, y) = xy+e^(-x^2-y^2)#?
• What are the extrema and saddle points of #f(x, y) = xy(1-x-y)#?
• What are the extrema of #f(x) = x^3 - 27x#?
• What are the extrema of #f(x) = 8 - 2x# for #x>=6#?
• What are the extrema of #x^3-2x^2-8x#?
• What are the extrema of #y = x^4 - 3x^3 + 3x^2 - x#?
• What are the extrema and saddle points of #f(x,y) = e^y(y^2-x^2)#?
• What are the extrema and saddle points of #f(x,y) = xy(e^(y^2)-e^(x^2))#?
• What are the extrema and saddle points of #f(x,y) = x^2+xy+y^2+y#?
• What are the extrema and saddle points of #f(x)=2x^2 lnx#?
• What are the extrema of #f(x)=2x^3-3x^2-36x-3#?
• What are the extrema of #f(x)=2x+1#?
• What are the global and local extrema of #f(x)=x^3-3x+6# ?
• What are the global and local extrema of #f(x)=x^3+48/x# ?
• What are the extrema of #f(x)= x+sinx in [-pi,pi]# ?
• What are the global and local extrema of #f(x)=4x-x^2 # ?
• What are the global and local extrema of #f(x) = x^3-9x+3 # ?
• What are the global and local extrema of #f(x) = e^x(x^2+2x+1) # ?
• What are the global and local extrema of #f(x)=8x^3-4x^2+6# ?
• What are the global and local extrema of #f(x)=x^3-x^2-x# ?
• What are the global and local extrema of #f(x)=x^3-x^2-x+1# ?
• What are the global and local extrema of #f(x)=x^2 -2x +3# ?
• What are the local extrema an saddle points of #f(x,y) = x^2 + xy + y^2 + 3x -3y + 4#?
• What are the global and local extrema of #f(x)=x^3 + 4x^2 - 5x # ?
• What are the global and local extrema of #f(x)=2x^7-2x^5 # ?
• What are the global and local extrema of #f(x) = x^2(2 - x) # ?
• What are the extrema of # f(x)=x/(x^2+9)# on the interval [0,5]?
• What are the extrema of # f(x)=x/(x-2)# on the interval [-5,5]?
• What are the extrema of # f(x)=(x^2 -9)^3 +10# on the interval [-1,3]?
• What are the extrema of # f(x)=1/x^3 +10x# on the interval [1,6]?
• What are the absolute extrema of # f(x)= |sin(x) + ln(x)|# on the interval (0 ,9]?
• What are the absolute extrema of # f(x)= |sin(x) - cos(x)|# on the interval [-pi,pi]?
• What are the absolute extrema of # f(x)= x/(x^2 + 25)# on the interval [0,9]?
• What are the absolute extrema of # f(x)= x^(2)+2/x # on the interval [1,4]?
• What are the absolute extrema of # f(x)= 2 + x^2 in [-2, 3]#?
• What are the absolute extrema of # f(x)= 2x^2 - x +5 in [-1, 5]#?
• What are the absolute extrema of # f(x)= cos(1/x)−xsin(1/x) in [-1/pi,1/pi]#?
• What are the absolute extrema of # f(x)= x^3 -3x+1 in [0,3]#?
• What are the absolute extrema of # f(x)= x^5 -x^3+x^2-7x in [0,7]#?
• What are the absolute extrema of # f(x)= xsqrt(25-x^2) in [-4,5]#?
• What are the absolute extrema of # f(x)= xsqrt(4-x^2) -x# in #[-1,2]#?
• What are the absolute extrema of # f(x)= x-ln(3x) in [1,e]#?
• What are the absolute extrema of # f(x)= xe^(x^2)/128in [-5,16]#?
• What are the absolute extrema of # f(x)= 6x^3 − 9x^2 − 36x + 3 in [-4,8]#?
• What are the absolute extrema of # f(x)= 3x^3 − sqrt(3x^2 − 6x + 3) in [-2,9]#?
• What are the absolute extrema of #f(x)=x/(x^2+1) in(0,2)#?
• What are the absolute extrema of #f(x)=(x-3)/(x^2+x-7) in(0,5)#?
• What are the absolute extrema of #f(x)=x-sqrt(5x-2) in(2,5)#?
• What are the absolute extrema of #f(x)=2x^2 - 8x + 6 in[0,4]#?
• What are the absolute extrema of #f(x)=(2x^3-x)/((x^2-64)# in #[-8,8]# ?
• What are the absolute extrema of #f(x)=(x^4) / (e^x) in[0,oo]#?
• What are the absolute extrema of #f(x)=(sinx) / (xe^x) in[ln5,ln30]#?
• What are the absolute extrema of #f(x)=(x^2 - 1)^3 in[-oo,oo]#?
• What are the absolute extrema of #f(x)=1/(1+x^2) in[oo,oo]#?
• What are the absolute extrema of #f(x)=(x-1)/(x^2+x+2) in[oo,oo]#?
• How do I find the absolute minimum and maximum of a function using its derivatives?
• What are the absolute extrema of #f(x)=x / (x^2 -6) in[3,7]#?
• What are the absolute extrema of #f(x)=sin2x + cos2x in[0,pi/4]#?
• What are the absolute extrema of #f(x)=2xsin^2x + xcos2x in[0,pi/4]#?
• What are the absolute extrema of #f(x)=x^(1/3)*(20-x)in[0,20]#?
• What are the absolute extrema of #f(x)=(x^3-7x^2+12x-6)/(x-1)in[1,4]#?
• What are the absolute extrema of #f(x)=x - e^x in[1,ln8]#?
• What are the absolute extrema of #f(x)=x / e^(x^2) in[1,oo]#?
• What are the absolute extrema of #f(x)=2x^3-15x^2 in[-2,10]#?
• What are the absolute extrema of #f(x)=9x^(1/3)-3x in[0,5]#?
• What are the absolute extrema of #f(x)=(9x^(1/3))/(3x^2-1) in[2,9]#?
• What are the absolute extrema of #f(x)=(x-2)(x-5)^3 + 12in[1,4]#?
• What are the absolute extrema of #f(x)=5x^7 - 7x^5 - 5 in[-oo,oo]#?
• What are the absolute extrema of #f(x)=(6x) / (4x+8) in[-oo,oo]#?
• What are the absolute extrema of #f(x)=8x^3 - 24x + 3 in[-oo,oo]#?
• What are the absolute extrema of #f(x)=(x+1)(x-8)^2+9 in[0,16]#?
• What are the absolute extrema of #f(x)=x^3 - 3x + 1 in[0,3]#?
• What are the absolute extrema of #f(x)=2cosx+sinx in[0,pi/2]#?
• What are the absolute extrema of #f(x) =x/(x^2-x+1) in[0,3]#?
• What are the absolute extrema of #f(x) =x^4 − 8x^2 − 12 in[-3,-1]#?
• What is the minimum value of #g(x) = x/csc(pi*x)# on the interval #[0,1]#?
• What is the minimum value of #g(x) = x^2+ 12x + 11?# on the interval #[-5,0]#?
• What is the minimum value of #g(x) = x^2-2x - 11/x?# on the interval #[1,7]#?
• What is the minimum value of #g(x) = (x-1)/(x^2+4)?# on the interval #[-2,2]#?
• What are the extrema of #g(x) = cos^2x+sin^2x?# on the interval #[-pi,pi#?
• What are the extrema of #g(x) = 5x-80?# on the interval #[-1,10]#?
• What are the extrema of #f(x)=3x-1/sinx # on #[pi/2,(3pi)/4]#?
• What are the extrema of #f(x)=-8x^2+x# on #[-4,8]#?
• What are the extrema of #f(x)=x^2+2x+15# on #[-oo,oo]#?
• What are the extrema of #f(x)=5x^2+4x-3# on #[-oo,oo]#?
• What are the extrema of #f(x)=-2x^2+4x-3# on #[-oo,oo]#?
• What are the extrema of #f(x)=3x^2 - 12x + 13# on #[-oo,oo]#?
• What are the extrema of #f(x)=-3x^2+30x-74# on #[-oo,oo]#?
• What is the absolute minimum of #f(x)=xlnx#?
• What are the extrema of #f(x)=x^2 - 8x + 12# on #[-2,4]#?
• What are the extrema of #f(x)=(x - 4)(x - 5)# on #[4,5]#?
• What are the extrema of #f(x) = e^(-x^2)# on #[-.5, a] #, where #a > 1 #?
• What are the extrema of #f(x)=4x^2-24x+1#?
• What are the extrema of #f(x)=f(x)= -x^2+8x+7#?
• What are the extrema of #f(x)=f(x)= x^2 -4x +3#?
• What are the extrema of #f(x)=3+ 2x -x^2#?
• What are the extrema of #f(x)=-x^2 +5x -1 #?
• What are the extrema of #f(x)=x^2-192x+8 # on #x in[-4,9]#?
• What are the extrema of #f(x)=(x^2)/(x^2-3x)+8 # on #x in[4,9]#?
• What are the extrema of #f(x)=x^2 - 6x + 11 # on #x in[1,6]#?
• What is the minimum value of #f(x)=3x^2-6x+12#?
• What are the extrema of #f(x) = 3x^2 + 12x + 16#?
• What are the extrema of #g(x) = 2 sin(2x - pi) + 4# on #[-pi/2,pi/2]#?
• What are the local extema of #f(x)=x^2-4x-5#?
• What are the local extrema of #f(x)=(x-3)(x^2-2x-5)#?
• What are the local extrema of #f(x)=(x-1)/(x-4)#?
• What are the local extrema of #f(x)=x^2/lnx#?
• What are the local extrema of #f(x)= x^2/(x^2-3x-5) #?
• What are the local extrema of #f(x)= xe^-x#?
• What are the local extrema of #f(x)= e^(x^2)-x^2e^x#?
• What are the local extrema of #f(x)= x^3-7x#?
• What are the local extrema of #f(x)= (x^5-x^2-4)/(x^3-3x+4)#?
• What are the local extrema of #f(x)= x/((x-2)(x-4)^3)#?
• What are the local extrema of #f(x)= ((x-2)(x-4)^3)/(x^2-2)#?
• What are the local extrema of #f(x)= xsqrt(x+3/x)#?
• What are the local extrema of #f(x)= 1/sqrt(x^2+e^x)-xe^x#?
• What are the local extrema of #f(x)= lnx/e^x#?
• What are the local extrema of #f(x)= e^xln1^x#?
• What are the local extrema of #f(x)= xlnx-xe^x#?
• What are the local extrema of #f(x)= 1/x-1/x^3+x^5-x#?
• What are the local extrema of #f(x)= (x^3-x^2-5x+4)/(x-2)^2#?
• What are the local extrema of #f(x)= (3x^3-2x^2-2x+43)/(x-1)^2+x^2#?
• What are the local extrema of #f(x)= x^3-x+3/x#?
• What are the local extrema of #f(x)= 4x^2-2x+x/(x-1/4)#?
• What are the local extrema of #f(x)= x^2(x+2)#?
• What are the local extrema of #f(x)= x^3-3x^2-9x+7#?
• What are the local extrema of #f(x)= -2x^2 + 9x#?
• What are the local extrema of #f(x)= x^3 - 3x^2 - x + 1#?
• What are the local extrema of #f(x)= x^3 - 9x^2 + 19x - 3 #?
• What are the local extrema of #f(x)= x^3-6x^2+15#, if any?
• What are the local extrema, if any, of #f(x)= 4x+6/x #?
• What are the local extrema, if any, of #f(x)= (4x-3)^2-(x-4)/x #?
• What are the local extrema, if any, of #f(x)= 2x+15x^(2/15)#?
• What are the local extrema, if any, of #f(x)= x^2-1#?
• What are the local extrema, if any, of #f(x)= 2x^3 – 6x^2 – 48x + 24#?
• What are the local extrema, if any, of #f(x)= –2x^3 + 6x^2 + 18x –18#?
• What are the local extrema, if any, of #f(x)= (x^2 + 6x-3)*e^x + 8x –8#?
• What are the local extrema, if any, of #f(x)= 120x^5 - 200x^3#?
• What are the local extrema, if any, of #f (x) = x^3 - 6x^2 - 15x + 11 #?
• What are the local extrema, if any, of #f (x) = x^4-8x^2-48 #?
• What are the local extrema, if any, of #f (x) = x^3-12x+2 #?
• What are the local extrema, if any, of #f (x) = 2x^4-36x^2+5 #?
• What are the local extrema, if any, of #f (x) =2ln(x^2+3)-x#?
• What are the local extrema, if any, of #f (x) =x^3-3x+6#?
• What are the local extrema, if any, of #f (x) =(x^3-3)/(x+6)#?
• What are the local extrema, if any, of #f (x) =x^3+3x^2-5x#?
• What are the local extrema, if any, of #f (x) =(x^3+3x^2)/(x^2-5x)#?
• What are the local extrema, if any, of #f (x) =xe^(x^3-7x)#?
• What are the local extrema, if any, of #f (x) =x^2-2x+4#?
• What are the local extrema, if any, of #f (x) =(x^2-2x)^3+(4x^2-3x^4)*e^(2x)#?
• What are the local extrema, if any, of #f (x) =x/(-12x+2#?
• What are the local extrema, if any, of #f (x) =(x+1)^7/2#?
• What are the local extrema, if any, of #f (x) =(x^3−4 x^2-3)/(8x−4)#?
• What are the local extrema, if any, of #f (x) =a(x-2)(x-3)(x-b)#, where #a# and #b# are integers?
• What are the local extrema, if any, of #f (x) =(lnx)^2/x#?
• What are the local extrema, if any, of #f (x) =(xlnx)^2/x#?
• What are the local extrema, if any, of #f (x) =(x^3 + 2x^2)/(3 - 5x)#?
• What are the local extrema, if any, of #f (x) =sqrt(4-x^2)#?
• What are the local extrema, if any, of #f (x) =80+108x-x^3 #?
• What are the local extrema of #f(x) = x^3 - 3x^2 - 9x +1#?
• What are the local extrema, if any, of #f(x) =x^2 + 9x +1 #?
• What are the local extrema, if any, of #f(x) =x^2(x+2) #?
• What are the local extrema, if any, of #f(x) =2x^3 -3x^2+7x-2 #?
• What are the local extrema, if any, of #f(x) =(lnx-1)^2 / x#?
• What are the local extrema, if any, of #f(x) =2-x^2#?
• How do you find the relative extrema for #f(x)=(9x^(2)+1)/x#?
• How do you find the relative extrema for #y=x^3#?
• How do you find local maximum value of f using the first and second derivative tests: #f(x)= sinx#?
• What is the relative minimum, relative maximum, and points of inflection of #f(x) = x^4 - 4x^2#?
• How do you find the axis of symmetry, graph and find the maximum or minimum value of the function #f(x)=-x^2+6x+6#?
• What is the relative maximum of y = csc (x)?
• How do you find the exact relative maximum and minimum of the polynomial function of #g(x) = x^3 - 3x^2 - 9x +1#?
• How do you find the local extremas for #f(x)=xe^x#?
• How do you find the local extremas for # f(x)= (x-3)^3#?
• How do you find the local extremas for #g(x) = x^2 + 1#?
• How do you find the local extremas for #g(x) = - |x+6|#?
• How do you find the local extrema for #f(x) = 3x^5 - 10x^3 - 1# on the interval [-1,1]?
• How do you find the local extrema for #y=4x^3 + 7#?
• How do you find the local extremas for #x(x-1)# on [0,1]?
• How do you find the local extremas for #f(x)=2x + (5/x) #?
• How do you find the local extremas for #f(x)=x^(1/3)(x+8)#?
• How do you find the local extrema for # f(x) = (3x + 4)^(-3/4) #?
• How do you find the local extrema for #f(x)=5x-x^2#?
• How do you find the local extrema for # (x^2)(e^-x) # from [-2,4]?
• How do you find the local extrema for #y=sqrtx/(x-5)#?
• How do you find the local extrema for #f(x) = 2-2x^2# on domain #-1 <= x <= 1#?
• How do you find the local extrema for #y = [1 / x] - [1 / (x - 1)]#?
• How do you find the local extrema for #f(x)=-0.12x^3 + 900x - 830#?
• How do you find the local extrema for #(e^x)(x^2)#?
• How do you find the local extrema for #f(x) = x sqrt( x - 3 )#?
• How do you find the local extrema for #f(x) = x - ln(x)# on [0.1,4]?
• How do you find the local extrema for #f(x) = (x-3)^3# on (-∞, ∞)?
• How do you find the local extrema for #f(x)= x^4-4x³#?
• How do you find the local extrema for #f(x)=(x-3)(x-1)(x+2)#?
• How do you find the local extrema for #f(x) = 2x^3 - x^2 - 4x +3#?
• How do you find the local extrema for #F(x)= sin (x + (π/2) )#?
• Question #4a6db
• How do you find the absolute extreme values of each function on the interval #y = 10 - 8x^2# on [-1,2]?
• How to find the max and minimum of #f(x)= abs(x-1 )+ 2abs(x+5) + 3abs(x-4)# using derivatives?
• How do you find the local extrema of #f(x)=x^3-6x#?
• How do you find the local extrema of #g(x)=-x^4+2x^2#?
• Question #31214
• What is the derivative of #y = ln(cscx)#?
• Question #64b09
• Calculus 1 absolute minimum and maximum of a function?
• What is the maximum value of #(3-cosx)/(1+cosx)# for #0< x < (2pi)#?
• Given #f(x) = -2(x+2)(x-1)^2# on the open interval (-3,3). How do you determine the x coordinate of the relative minimum of f (x) in the open interval (-3,3)?
• Question #115fc
• A differentiable function #f# has only one critical number: #x=-3#. Identify the relative extrema of #f# at (-3, f(-3)) if #f'(-4)=(1/2)# and #f'(-2)=-1#?
• Does the function #f(x)= -x^2+6x-1# have a minimum or maximum value?
• What is the minimum of #f(x)=|x-1|+|x-2|+cdots+|x-1391|# function?
• Find the absolute maximum and absolute minimum values of #f(x) = x^(1/3) e^(−x^2/8)# on the interval [−1, 4]?
• Question #a681a
• Question #eb2b6
• Question #cf6e2
• What is the difference between 'relative maximum(or minimum)' and 'absolute maximum(or minimum)' in functions?
• Question #3d707
• The graph of #y=ax^2+bx# has an extremum at #(1,-2)#. Find the values of a and b?
• Can someone help me with this question ? i cant find the derivatives or the others !! someone help me please ?