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The function $\"\"$ , $\"\"$ .

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Maximum value of a function exist either at the end points or at the critical points.

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First evaluate the function at the end points.

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

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$\"\"$

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

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$\"\"$

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Find the critical points.

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$\"\"$ is differentiable at all points because its a polynomial.

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Therefore $\"\"$ are the only critical points.

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

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$\"\"$

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To find out critical points equate $\"\"$ to zero

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$\"\"$

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$\"\"$ and $\"\"$ and $\"\"$ .

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$\"\"$ and $\"\"$ and $\"\"$ .

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$\"\"$ and $\"\"$ and $\"\"$ .

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$\"\"$ and $\"\"$ and $\"\"$ .

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Therefore the critical points are $\"\"$ , $\"\"$ and $\"\"$ .

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Find the absolute maximum value.

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

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$\"\"$

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$\"\"$ .

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Since $\"\"$ and $\"\"$ are positive numbers, $\"\"$ .

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Absolute maximum is $\"\"$ .

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Absolute maximum is $\"\"$ .

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