$\"\"$

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The function is $\"\"$ .

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Consider $\"\"$ .

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Derivative on each side by $\"\"$ .

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$\"\"$

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Apply the power rule of derivative : $\"\"$ .

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$\"\"$

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$\"\"$

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To examine the behavior of a function, equate the derivative to zero.

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$\"\"$

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The $\"\"$ values are $\"\"$ and $\"\"$ .

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$\"\"$

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The function is $\"\"$ .

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The domain of the function is $\"\"$ .

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There are four regions to examine the behavior of the function.

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First region $\"\"$ .

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Consider a test point $\"\"$ in the region.

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$\"\"$ .

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The derivative is negative, the function is decreasing over $\"\"$ .

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Second region $\"\"$ .

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Consider a test point $\"\"$ in the region.

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$\"\"$ .

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The derivative is positive, the function is increasing over $\"\"$ .

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Third region $\"\"$ .

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Consider a test point $\"\"$ in the region.

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$\"\"$

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The derivative is negative, the function is decreasing over $\"\"$ .

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Fourth region $\"\"$ .

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Consider a test point $\"\"$ in the region.

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$\"\"$

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The derivative is positive, the function is increasing over $\"\"$ .

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A monotonic function is increasing over $\"\"$ and $\"\"$ .

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A monotonic function is decreasing over $\"\"$ and $\"\"$ .

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Therefore the function is not strictly monotonic.

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$\"\"$

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The function is not strictly monotonic.