$\"\"$

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The function is $\"\"$ .

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Rewrite the function.

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$\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$

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Again apply derivative on each side with repect to $\"\"$ .

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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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$\"\"$

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The function $\"\"$ is always positive.

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The concavity depends on $\"\"$ .

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$\"\"$ for the interval $\"\"$ , then the function is concave upward in the interval $\"\"$ .

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$\"\"$ for the interval $\"\"$ , then the function is concave downward in the interval $\"\"$ .

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$\"\"$

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The function is concave upward in $\"\"$ and concave downward in $\"\"$ .