$\"\"$

(a)

The function is $\"\"$ .

Find the critical numbers by applying derivative.

$\"\"$ .

Apply derivative on each side with respect to $\"\"$ .

$\"\"$

$\"\"$ .

Equate $\"\"$ to $\"\"$ .

$\"\"$

$\"\"$ and $\"\"$

$\"\"$ and $\"\"$ .

Critical numbers are $\"\"$ and $\"\"$ .

$\"\"$

(b)

Consider the test intervals to find the interval of increasing and decreasing.

Critical points are $\"\"$ and $\"\"$ .

The test intervals are $\"\"$ , $\"\"$ and $\"\"$ .

\ \

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

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

The function is decreasing on the interval $\"\"$ .

$\"\"$

(c)

First derivative test to identify all relative extrema.

From the first derivative test the function $\"\"$ changing from positive to negative at $\"\"$ . [ from (b)]

$\"\"$ has a relative maximum at $\"\"$ .

$\"\"$

So the function $\"\"$ has relative maximum at $\"\"$ .

From the first derivative test the function $\"\"$ changing from negative to positive at $\"\"$ . [ from (b)]

$\"\"$ has a relative minimum at $\"\"$ .

$\"\"$

So the function $\"\"$ has relative minimum at $\"\"$ .

$\"\"$

(d)

Graph :

Graph the function $\"\"$ :

$\"\"$

Observe the graph :

The function has critical numbers at $\"\"$ and $\"\"$ .

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

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

$\"\"$

(a) The function has critical numbers at $\"\"$ and $\"\"$ .

(b) The function $\"\"$ is increasing on the interval $\"\"$ and $\"\"$ and decreasing on the interval $\"\"$ .

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

(d) Graph of the function $\"\"$ is

$\"\"$ .