$\"\"$

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No, it does not follow that $\"\"$ even though the function is continuous on $\"\"$ and differentiable on $\"\"$ and there exists $\"\"$ in $\"\"$ such that $\"\"$ .

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Consider a function is $\"\"$ over the interval $\"\"$ .

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The function is continuous on $\"\"$ and differentiable on $\"\"$ .

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$\"\"$

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

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$\"\"$

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Therefore $\"\"$ .

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$\"\"$

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Find $\"\"$ .

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$\"\"$

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$\"\"$

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So here for this example $\"\"$ .

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$\"\"$

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No, it does not follow that $\"\"$ .