Question bank/JEE Main/Mathematics

The function f(x) = maximum
$\left\{ \sqrt{x(2 - x)},2 - x \right\}$ is non-differentiable at x
equal to

A0, 1B1, 3C2, 3D1, 2

Show answer and solution▾

[IMAGE] At x = 2
L.H.D$= h\overset{Lt}{\rightarrow}0^{+}\frac{\sqrt{(2 - h)(2 - (2 - h))} - 0}{- h}$
$= h\overset{Lt}{\rightarrow}0^{+}\frac{\sqrt{2 - h}}{- \sqrt{h}}\left( \frac{\sqrt{2}}{0}\ form\ \right)$
= not finite.

Source: Grass-G / M-11 Mathematics Paper-2 1Nov.docx