$\"\"$

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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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$\"\"$

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The function is $\"\"$ .

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The function $\"\"$ is continuous on the interval $\"\"$ , because it is a polynomial.

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Differentiate $\"\"$ on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$ is not differentiable at $\"\"$ , but it is differentiable on the open interval $\"\"$ , which satisfies the Rolle $\"\"$ s Theorem.

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$\"\"$

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Check $\"\"$ at the end points :

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

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$\"\"$

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

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$\"\"$

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$\"\"$ , hence Rolle $\"\"$ s theorem is applicable on $\"\"$ .

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$\"\"$

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Find the value of $\"\"$ , such that $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$ .