How do you find the local max and min for # f(x)=x^32x+5# on the interval (2,2)?
See below.
Plugging these values into the second derivative, will allow us to find whether these are maximum, minimum or points of inflection. Using the following, if:
The second derivative is the derivative of the first derivative.
GRAPH:
graph{y=x^32x+5 [5, 5, 20, 20]}
By signing up, you agree to our Terms of Service and Privacy Policy
To find the local maximum and minimum of ( f(x) = x^3  2x + 5 ) on the interval ((2, 2)), follow these steps:

Compute the derivative of ( f(x) ) to find critical points. [ f'(x) = 3x^2  2 ]

Set ( f'(x) = 0 ) and solve for ( x ) to find critical points. [ 3x^2  2 = 0 ] [ x^2 = \frac{2}{3} ] [ x = \pm \sqrt{\frac{2}{3}} ]

Evaluate ( f(x) ) at the critical points and endpoints of the interval ((2, 2)). [ f\left(\sqrt{\frac{2}{3}}\right), \quad f\left(\sqrt{\frac{2}{3}}\right), \quad f(2), \quad f(2) ]

Compare the values of ( f(x) ) at critical points and endpoints to determine local maxima and minima.
After evaluating, you'll find:
[ f\left(\sqrt{\frac{2}{3}}\right) \approx 6.50 ] [ f\left(\sqrt{\frac{2}{3}}\right) \approx 3.50 ] [ f(2) = 13 ] [ f(2) = 5 ]
The minimum occurs at ( x = \sqrt{\frac{2}{3}} ) and the maximum occurs at ( x = 2 ).
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 Is #f(x)=(x+3)(x2)(x2)# increasing or decreasing at #x=2#?
 How do you find the absolute and local extreme values for #f(x)=(x3)^29# on the interval [8,3]?
 Is #f(x)=(2x^3x^25x+2)/(x+1)# increasing or decreasing at #x=0#?
 What are the local extrema, if any, of #f(x) =2x^3 3x^2+7x2 #?
 What are the critical values, if any, of # f(x)= (x2)/(x^24)+2x#?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7