(a)

The function is .

Find the critical numbers by applying derivative.

Apply derivative on each side with respect to .

Equate the derivative to .

Therefore the critical numbers is .

(b)

Consider the test intervals to find the interval of increasing and decreasing.

Test intervals are  and .

Test interval	Test value	Sign of	Conclusion
		\ \	Decreasing
		\ \	Increasing

The function  is increasing on the interval .

The function  is decreasing on the interval .

(c)

Use first derivative test to identify all relative extrema.

 changes from negative to positive at . [From (b) ]

Therefore according to First derivative test , the function has minimum at .

The function  has a relative maximum at .

Find .

So the function  has relative minimum at .

(d)

Graph :

Graph the function is  :

Observe the graph :

The function has critical numbers  is .

The function  is increasing on the interval .

The function  is decreasing on the interval .

The function  has relative minimum at .

(a) The function has critical numbers  is .

(b)

The function  is increasing on the interval .

The function  is decreasing on the interval .

(c) The function  has relative minimum at .

(d) Graph of the  function is  is

.