Step 1:

The function

and

and

The critical points are and the test intervals are .

Step 2:

First derivative test:

Interval	Test Value	Sign of	Conclusion
			Decreasing
			Increasing
			Decreasing

is changes its sign from negative to positive, hence f has a local minimum at .

Local minimum is  . 

is changes its sign from positive to negative, hence f has a local maximum at . 

Local maximum is .

Step 3:

Second derivative test:

Differentiate with respect to x:

, curve is concave up, thus is a local minimum.

Local minimum is  .

, curve is concave down, thus is a local minimum.

Local maximum is .

Solution:

Local minimum is  .

Local maximum is .