# The derivative of a function f is given by f'(x)= (x-3)e^x for x>0 and f(x)=7? a.) The function has a critical point at x=3. At this point, does f have a relative minimum or neither?

##### 1 Answer

Dec 9, 2016

The function

#### Explanation:

To find if a function has a critical point at a place where

- Minimum if
#f'(x)# changes sign from negative to positive - Maximum if
#f'(x)# changes sign from positive to negative.

To check it you can calculate the second derivative: