$\"\"$

(a)

The function is $\"\"$ .

Find the critical numbers by applying derivative.

$\"\"$

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

$\"\"$

Equate the derivative to $\"\"$ .

$\"\"$

Therefore the critical number is $\"\"$ .

$\"\"$

(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 $\"\"$ .

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(c)

Use first Derivative Test to identify all relative extrema.

$\"\"$ changes from positive to negative . [From (b) ]

Therefore according to First derivative test , the function has maximum at $\"\"$ .

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

Find $\"\"$ .

$\"\"$

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

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(d)

Graph the function is $\"\"$ .

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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 $\"\"$ .

$\"\"$

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

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

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

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