$\"\"$

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

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The function $\"\"$ is continuous over closed interval $\"\"$ , and differentiable on the open interval $\"\"$ .

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Therefore mean value theorem can be applied.

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So, there exists at least one number $\"\"$ in $\"\"$ such that $\"\"$ .

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The slope of the secant line through $\"\"$ and $\"\"$ is

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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The function is $\"\"$ .

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

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$\"\"$

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$\"\"$

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Result of mean value theorem : $\"\"$ .

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$\"\"$

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For $\"\"$ .

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$\"\"$

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$\"\"$ is in the given interval $\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$ .