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The value of ‘ $c$ ’ in Lagrange's mean value theorem for $f (x) = l x^{2} + m x + n, (l \neq 0)$ on $[a, b]$ is

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$\frac{a}{2}$

$\frac{b}{2}$

$\frac{(a - b)}{2}$

$\frac{(a + b)}{2}$

answer is D.

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Detailed Solution

$f^{'} (c) = \frac{l b^{2} + m b + n - l a^{2} - m a - n}{b - a}$

$\Rightarrow 2 l c + m = l (a + b) + m \Rightarrow c = \frac{a + b}{2}$

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