$\"\"$

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

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Rolle $\"\"$ s Theorem :

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Let $\"\"$ be a function that satisfies the following three hypotheses.

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1. $\"\"$ is continuous on $\"\"$ .

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2. $\"\"$ is differentiable on $\"\"$ .

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3. $\"\"$ .

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Then there is a number $\"\"$ in $\"\"$ such that $\"\"$ .

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The function $\"\"$ continuous over $\"\"$ .

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

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$\"\"$

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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Therefore $\"\"$ .

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Hence function $\"\"$ satisfy the Rolle $\"\"$ s theorem.

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$\"\"$

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There exist at least one $\"\"$ value in the interval $\"\"$ ,such that $\"\"$ .

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$\"\"$ .

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Apply derivative with respect to $\"\"$ .

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$\"\"$

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Equate it to zero.

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$\"\"$

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If $\"\"$ then $\"\"$ .

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If $\"\"$ , $\"\"$ .

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$\"\"$ is not in the interval $\"\"$ .

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

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$\"\"$

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The function $\"\"$ satisfy the Rolle $\"\"$ s theorem.

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The value of $\"\"$ .