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Consider the function $f (x) = 8 x^{2} - 7 x + 5$ on the interval $[- 6, 6] .$ the value of c satisfying the conclusion of Lagrange’s mean value theorem is ______________.

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Detailed Solution

$f^{'} (c) = 16 c - 7$

$= \frac{f (6) - f (- 6)}{12}$

$= \frac{(8 \times 36 - 7 \times 6 + 5) - (8 \times 36 - 7 \times 6 + 5)}{12}$

$= - \frac{2 \times 7 \times 6}{12} = - 7$

$\Rightarrow c = 0$

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