# How do you use the second derivative test to find the local extrema for #f(x)=e^(x^2)#?

##### 1 Answer

Apr 4, 2018

The function

#### Explanation:

Evaluate the first and second derivatives of the function:

Solving the equation:

as the exponential is never null we can see that the only critical point for the function is

Then we see that;

so that the critical point is a local minimum.

graph{e^(x^2) [-2, 2, -1, 10]}