(a)

The function is .

Find the critical numbers by applying derivative .

Equate it to zero .

The critical number is .

Consider the test intervals to find the interval.

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

(b)

Use first derivative test to identify all relative extrema.

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

Therefore according to first derivative test , the function has maximum at .

When  , .

The relative maximum point is .

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

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

When  , .

The relative minimum point is .

(c)

Graph the function  to verify the above result .

(a)  is increasing over intervals  and .

      is decreasing over interval .

(b) The relative maximum point is .

       The relative minimum point is .

(c)

.