Compute the derivative of the function
Set the derivative equal to zero
Solve for the critical points
Find where the derivative does not exist
Evaluate the second derivative at each critical point
If the second derivative is negative, the point is a local maximum
If the second derivative is positive, the point is a local minimum
If the second derivative is zero, use another test
Check the sign change of the first derivative around each critical point
If the first derivative changes from positive to negative, the point is a local maximum