SOLUTION: For the function f(x) = −5x^3 + 3x^5 , find all critical values and determine whether each represents a local maximum, local minimum or neither. Then find the absolute extrem

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Question 1123975: For the function f(x) = −5x^3 + 3x^5 , find all critical values and determine whether each represents a local maximum, local minimum or neither. Then find the absolute extrema on the interval [−2, 2].
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
"Critical values"?


df%2Fdx=-15x%5E2%2B15x%5E4

15x%5E4-15x%5E2=0
x%5E4-x%5E2=0
x%5E2%28x%5E2-1%29=0
x%5E2%28x-1%29%28x%2B1%29=0

The local extreme points are at x of -1, 0, and 1.

Maximum at x=-1, minimum at x=1.
Inflexion which is not an extreme point for x at 0.

You may be able to use second-derivative to help with these.