$\"\"$

(a)

The function is $\"\"$ .

Find the critical numbers by applying derivative.

$\"\"$

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

$\"\"$

Equate the derivative to $\"\"$ .

$\"\"$

For $\"\"$ .

$\"\"$

Equate the derivative to $\"\"$ .

$\"\"$

But $\"\"$ is not in the domain of $\"\"$ .

Therefore $\"\"$ is not considered as a critical number.

The function has a discontinuity at $\"\"$ .

Therefore the the point $\"\"$ treated as critical point for the function $\"\"$ .

$\"\"$

(b)

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

Test intervals are $\"\"$ and $\"\"$ .

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

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

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

$\"\"$

(c)

Use first derivative test to identify all relative extrema.

At the critical point $\"\"$ , the function is discontinuous.

So need a graphing calculator to find the relative extreme.

$\"\"$

(d)

Graph the function is $\"\"$ .

$\"\"$

The graph of the function has a relative maximum at $\"\"$ .

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

$\"\"$

(a)

Critical number is $\"\"$ .

(b)

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

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

(c)

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

(d)

Graph of the function is $\"\"$ .

$\"\"$ .