# How do you find local maximum value of f using the first and second derivative tests: #f(x) = e^x(x^2+2x+1)#?

##### 1 Answer

#### Explanation:

For a local maximum or minimum of

Applying the product rule and the standard differential of

Setting

Since

To test for a maximum or minimum we need to test the sign of

Applying the product rule and the standard differential of

We are asked to find the local maximum.

The local extrema can be seen on the graph of

graph{e^x(x^2+2x+1) [-4.783, 0.086, -1.156, 1.277]}