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Let $\"\"$ .

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Graph of $\"\"$ is given.

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(a) Determine $\"\"$ for $\"\"$ and $\"\"$ .

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Find $\"\"$ .

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$\"\"$ .

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Property of definite integral: $\"\"$ .

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Therefore, $\"\"$ .

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$\"\"$

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Find $\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$ .

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Find $\"\"$ .

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$\"\"$ \ \ Definite integral property: $\"\"$ .

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$\"\"$

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$\"\"$ .

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Find $\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Find $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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(b)

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$\"\"$ is derivative graph of the function $\"\"$ .

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From the derivative properties, whenever the derivative function is positive, then the original function is increasing.

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From the graph, $\"\"$ is positive in the $\"\"$ .

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Therefore, the function $\"\"$ is increasing on $\"\"$ .

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(c)

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From the results in part (a), it is clear that the function $\"\"$ has the maximum value at $\"\"$ .

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(d)

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Rough graph of the function $\"\"$ :

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Plot the points for $\"\"$ and $\"\"$ .

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$\"\"$

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(a) $\"\"$ , $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

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(b)

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

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(c)

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The function $\"\"$ has the maximum value at $\"\"$ .

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(d)

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$\"\"$ .