How do you find the local extremas for #f(x)=xe^x#?
There is a relative minimum at the point
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