Answer:
Option A
Explanation:
Given ,
f(x) =x for x≤ 0
=0 for x >0
for continuity at x=0
LHS at x=0 $\lim_{x \rightarrow 0^{-}}f(x)= \lim_{x \rightarrow0}x$
$\lim_{h \rightarrow 0^{-}}(0-h)=0 $ and RHL at x=0
$\lim_{x \rightarrow 0^{+}} f(x)= \lim_{x \rightarrow 0^{+}} 0=0$
Also, f(0)=0
$\therefore$ LHL=RHL=f(0)
Hence, f(x) is continuous at x=0
For differentiability at x=0
f'(x)=1 for x ≤ 0, 0 for x >0
$\therefore$ f(x) is not differentiable at x=0
