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The value of ' $c$ ' in Lagrange's mean value theorem for $f (x) = (x - a)^{m} (x - b)^{n} in [a, b]$ is

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$\frac{m a + n b}{m + n}$

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

$\frac{a + b}{m + n}$

$\frac{m b + n a}{m + n}$

answer is A.

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Detailed Solution

By Lagrange's theorem, $f^{'} (c) = \frac{f (b) - f (a)}{b - a} \Rightarrow c = \frac{m b + n a}{m + n}$

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