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#### karush

##### Well-known member

- Jan 31, 2012

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- Thread starter karush
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- Thread starter
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- Jan 31, 2012

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- Mar 1, 2012

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the MVT states there exists at least one value of $x \in (2,8)$ where $f'(x) = \dfrac{f(8)-f(2)}{8-2}$

$3 \le f'(x) \le 5 \implies 3 \le \dfrac{f(8)-f(2)}{8-2}\le 5 \implies 18 \le f(8)-f(2) \le 30$