$\"\"$

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(a)

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The function $\"\"$ and the interval is $\"\"$ .

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Find critical points.

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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The critical points exist when $\"\"$ .

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Equate $\"\"$ to zero.

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$\"\"$

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Therefore critical points are $\"\"$ .

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$\"\"$

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

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

Interval	Test Value	\ Sign of $\"\"$ \	Conclusion
$\"\"$	$\"\"$	\ $\"\"$ \	Decreasing
$\"\"$	$\"\"$	\ $\"\"$ \	Increasing
$\"\"$	$\"\"$	\ $\"\"$ \	Decreasing
$\"\"$	$\"\"$	\ $\"\"$ \	Increasing
$\"\"$	$\"\"$	\ $\"\"$ \	Decreasing
$\"\"$	$\"\"$	\ $\"\"$ \	Increasing
$\"\"$	$\"\"$	\ $\"\"$ \	Decreasing
$\"\"$	$\"\"$	\ $\"\"$ \	Increasing

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

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

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$\"\"$

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(b)

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The function $\"\"$ and the interval is $\"\"$ .

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From the first derivative test the function $\"\"$ changing from positive to negative at $\"\"$ .

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$\"\"$

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Relative maximum point is $\"\"$ .

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Similarly $\"\"$ has relative maximums at $\"\"$ and $\"\"$ .

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From the first derivative test the function $\"\"$ changing from negative to positive at $\"\"$ .

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$\"\"$

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Relative minimum point is $\"\"$ .

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Similarly $\"\"$ has relative minimums at $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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(c)

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Graph :

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The graph of the function $\"\"$ is

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$\"\"$

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$\"\"$

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(a)

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

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

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(b)

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Relative maximum point is $\"\"$ , $\"\"$ and $\"\"$ .

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Relative minimum point is $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

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(c)

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The graph of the function $\"\"$ is:

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$\"\"$ .