Step 1:

(a)

The function is .

Find the critical numbers by equating the first derivative to .

Apply derivative on each side with respect to .

Equate the derivative to .

So the function has critical number at .

Solution :

The function has critical number at .

Step 1:

(b)

The critical point is ,consider the table summarizes the testing of two intervals determined by the critical number.

Test interval
Test value
sign of
Conclusion	Increasing	\  Decreasing \

 So the function is increasing on the interval and decreasing on the interval .

Solution :

The function is increasing on the interval and decreasing on the interval .

Step 1:

(c)

Use first Derivative Test to identify all relative extrema.

The derivative of the function is .

The critical point is ,consider the table summarizes the testing of two intervals determined by the critical number.

Test interval
Test value
sign of
Conclusion	Increasing	\  Decreasing \

 From the fist derivative test the function changing from positive to negative at , then has a relative maximum at .

Find for .

So the function has relative maximum at .

Solution :

The function has relative maximum at .

Step 1:

(d)

Graph the function is .

Now observe the graph :

The function has critical number at .

The function is increasing on the interval and decreasing on the interval .

The function has relative maximum at .

Solution :

The function has critical number at .

The function is increasing on the interval and decreasing on the interval .

The function has relative maximum at .