(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

.