In [0, 1] Lagrange's mean value theorem is NOT applicable to - Vidyadip

MCQ

In $[0, 1]$ Lagrange's mean value theorem is $ NOT$ applicable to

✓
$f(x) = \left\{ {\begin{array}{*{20}{c}}
{\frac{1}{2} - x,\,\,\,\,\,\,\,\,\,x < \frac{1}{2}} \\
{{{\left( {\frac{1}{2} - x} \right)}^2},\,x \geqslant \frac{1}{2}}
\end{array}} \right.$
B
$f(x) = \left\{ {\begin{array}{*{20}{c}}
{\frac{{\sin x}}{x}\,\,x \ne 0} \\
{1,\,\,\,\,\,\,\,\,x = \frac{1}{2}}
\end{array}} \right.$
C
$f(x) = x|x|$
D
$f(x) = |x|$

✓

Answer

Correct option: A.

$f(x) = \left\{ {\begin{array}{*{20}{c}}
{\frac{1}{2} - x,\,\,\,\,\,\,\,\,\,x < \frac{1}{2}} \\
{{{\left( {\frac{1}{2} - x} \right)}^2},\,x \geqslant \frac{1}{2}}
\end{array}} \right.$

a
(a) The function defined in option $ (a) $ is not differentiable at $x = \frac{1}{2}$.

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