Determine the local maximum and minimum values of the function .
Stationary points occur when . First, find .
Now set equal to 0 and solve for .
Now evaluate the function at each point.
Therefore, the function has stationary points at and .
Finally, determine whether each point is a local minimum or a local maximum by evaluating the second derivative at each point.
Therefore, is a local minimum as is positive.
Therefore, is a local maximum as is negative.
Hence, the function has a local maximum value of and a local minimum value of .