$\"\"$

(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.

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

$\"\"$

(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)

$\"\"$ .