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?
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: