Find the derivative (f'(x))
Set (f'(x)=0) and solve for critical points
Find where (f'(x)) does not exist
Evaluate the function at all critical points
If the interval is closed, also evaluate the endpoints
Compare the function values
The largest value is a local maximum if it is greater than nearby values
The smallest value is a local minimum if it is less than nearby values
Use the first derivative test if needed
Use the second derivative test if needed
If (f”(c)>0), then (f(c)) is a local minimum
If (f”(c)<0), then (f(c)) is a local maximum
If (f”(c)=0), the test is inconclusive