# How do you find the local extremas for #f(x)=xe^x#?

##### 1 Answer

There is a relative minimum at the point

#### Explanation:

We can say that if

Therefore, the return points of the function

If the derivative is positive, we know that the function is increasing, whereas if the derivative is negative, then the function is decreasing.

When the derivative changes from negative to positive, the function has a local minimum, whereas if the change of sign is reversed, that is, from positive to negative, then the function has a local maximum.

In the case of the function

Equaling to zero we have:

It is easy to verify that, for values of

The