$\"\"$

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The function $\"\"$ .

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Let $\"\"$ .

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Find the $\"\"$ -intercepts by substituting $\"\"$ .

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$\"\"$ .

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Applying zero product property.

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

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

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$\"\"$ - intercepts are $\"\"$ and $\"\"$ .

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$\"\"$

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So $\"\"$ ,from rolles theorem we know that there exists at least one $\"\"$ 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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Product rule in derivatives $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Find the zeros of $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ is zero between $\"\"$ -intercepts at $\"\"$ .

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$\"\"$

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$\"\"$ -intercepts are $\"\"$ and $\"\"$ .

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$\"\"$ .