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Expression Formation

Consider the ...

Question

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

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Solution

The function is continuous as well as diffrentiable in the given interval, since it is a quadratic polynomial.
So, LMVT can be applied on the function.
So, $f^{'} (c) = \frac{f (6) - f (- 6)}{12}$
$\Rightarrow f^{'} (c) = \frac{(8 \times 36 - 7 \times 6 + 5) - (8 \times 36 + 7 \times 6 + 5)}{12} \Rightarrow f^{'} (c) = - 7$
$\Rightarrow 16 c - 7 = - 7 \Rightarrow c = 0$

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Expression Formation

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