(a)

The function is .

Find the critical numbers by applying derivative. \ \

Equate it to zero. \ \

Therefore the critical number is .

(b)

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

Test intervals are  and .

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

The function  is increasing on the interval .

The function  is decreasing on the interval .

(c)

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

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

When  , .

Therefore the relative minimum point is .

(d)

Graph :

Sketch the function  to verify the above result.

(a) The critical number is .

(b)  is decreasing over .

      is increasing over .

(c) Relative minimum point is .

(d) Graph of  the function  is

.