$\"\"$

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Draw the related diagram:

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$\"\"$

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

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Consider function $\"\"$ on interval $\"\"$ .

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To maximize $\"\"$ , minimize $\"\"$ .

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$\"\"$ .

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

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$\"\"$

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$\"\"$

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Apply derivative of inverse trigonometric functions formula: $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Find the critical numbers by equating derivative to zero.

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$\"\"$

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$\"\"$

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$\"\"$ .

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The critical number is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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The function $\"\"$ has minimum at $\"\"$ .

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Therefore, $\"\"$ is maximum at $\"\"$ .

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$\"\"$

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

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The absolute maximum is $\"\"$ .

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$\"\"$ is maximum at $\"\"$ .

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$\"\"$

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$\"\"$ is maximum at $\"\"$ .