$\"\"$

(a)

The function is $\"\"$ .

Rewrite the function as $\"\"$ .

Find the critical numbers by applying derivative.

$\"\"$

Equate it to zero.

$\"\"$

The critical numbers are $\"\"$ and $\"\"$ .

Consider the test intervals to find the interval.

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

The function $\"\"$ is increasing on the intervals $\"\"$ , $\"\"$ and $\"\"$ .

The function $\"\"$ is decreasing on the intervals $\"\"$ and $\"\"$ .

$\"\"$

(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 $\"\"$

$\"\"$

Relative maximum point is $\"\"$ .

Similarly $\"\"$ has relative maximum points at $\"\"$ .

$\"\"$ has relative minimum points at $\"\"$ and $\"\"$ .

$\"\"$

(c)

Graph the function $\"\"$ to verify the above result .

$\"\"$

(a)

The function $\"\"$ is increasing on the intervals $\"\"$ , $\"\"$ and $\"\"$ .

The function $\"\"$ is decreasing on the intervals $\"\"$ and $\"\"$ .

(b)

The function $\"\"$ has relative maximum points at $\"\"$ and $\"\"$ .

The function $\"\"$ has relative minimum points at $\"\"$ and $\"\"$ .

(c)

$\"\"$ .