$\"\"$

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(a)

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Consider $\"\"$ .

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$\"\"$

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The function $\"\"$ .

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Draw a coordinate plane.

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Graph the functions $\"\"$ and $\"\"$ in the same window.

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Graph :

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$\"\"$

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Observe the above graph :

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The function $\"\"$ represents the average value of $\"\"$ over the interval $\"\"$ .

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The graph of $\"\"$ greatest on $\"\"$ and the maximum occurs at $\"\"$ .

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$\"\"$

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(b)

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The function is $\"\"$ .

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$\"\"$

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Diffrentiate the function with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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To find critical values equate $\"\"$ to zero.

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$\"\"$

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$\"\"$

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Consider $\"\"$ .

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Again diffrentiate the function with respect to $\"\"$ .

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$\"\"$

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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By the second derivative test, the function $\"\"$ has a maximum value at $\"\"$ .

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$\"\"$

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(a)

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The function $\"\"$ represents the average value of $\"\"$ over the interval $\"\"$ and maximum occurs at $\"\"$ .

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(b)

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Maximum at $\"\"$ .