# How do you find the local max and min for # f(x)=x^3-2x+5# on the interval (-2,2)?

##### 1 Answer

See below.

#### Explanation:

First find the 1st derivative of

Maximum and minimum points have a horizontal gradient .i.e. gradient of

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.

Plugging in our values of

Both

GRAPH:

graph{y=x^3-2x+5 [-5, 5, -20, 20]}