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Q.

Lagrange’s mean value theorem cannot be applied for

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a

$f (x) = \log x$ in $[1, e]$

b

$f (x) = x - \frac{1}{x}$ in $[1, 3]$

c

$f (x) = \sqrt{x^{2} - 4}$ in $[2, 4]$

d

$f (x) = |x|$ in $[- 1, 2]$

answer is D.

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Detailed Solution

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$f (x) = |x|$ is not differentiable at $x = 0$

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