(D) Lagrange's Mean Value Theorem $(LMVT)$ states that for a function $f(x)$ to be applicable on $[a, b]$,it must be continuous on $[a, b]$ and differ

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(D) Lagrange's Mean Value Theorem $(LMVT)$ states that for a function $f(x)$ to be applicable on $[a, b]$,it must be continuous on $[a, b]$ and differentiable on $(a, b)$.Checking option $(d)$: $f(x) = |x|$.This function is continuous on $[0, 1]$,but it is not differentiable at $x = 0$,which lies within the interval $[0, 1]$.Therefore,$LMVT$ is not applicable to $f(x) = |x|$ on $[0, 1]$.

Class 12 Mathematics Continuity and Differentiation Rolle’s theorem, Lagrange's mean value theorem

Medium

In the interval $[0, 1]$,Lagrange's Mean Value Theorem is $NOT$ applicable to which of the following functions?

IIT 2003 All IIT

A
$f(x) = \begin{cases} \frac{1}{2} - x, & x < \frac{1}{2} \\ (\frac{1}{2} - x)^2, & x \ge \frac{1}{2} \end{cases}$
B
$f(x) = \begin{cases} \frac{\sin x}{x}, & x \neq 0 \\ 1, & x = 0 \end{cases}$
C
$f(x) = x|x|$
D
$f(x) = |x|$

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