A maximum would occur if the derivative exists and changes sign from positive to negative at a certain point.
A minimum would occur if the derivative exists and changes sign from negative to positive at a certain point.
This means the derivative must pass through zero to change the sign. So, equate your derivative to zero and solve for the x coordinates of these points. In Calculus, these points are called critical points.
Just in case you don't understand, I'd recommend the following resources: