(a)

The function is .

Find the critical numbers by applying derivative .

Equate it to zero.

Therefore the critical number is .

(b)

Now consider the test intervals to find the interval of increasing and decreasing.

Consider a number from .

Let in the interval .

Sign of is negative , hence is decreasing over .

Consider a number from .

Let

Sign of is positive , hence is increasing over .

(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) The relative minimum point is .

(d) Sketch the function is 

.