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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Which of the following functions is differentiable at $x=0$?
Solution
$|x|$ is not differentiable at $0$.
Near $x=0$, $\sin(|x|)\approx |x|$.
For option (4):
$f(x)=\sin(|x|)-|x|$
Near $0$:
$f(x)\approx |x|-|x|=0$
Both left-hand and right-hand derivatives at $0$ are equal, hence $f(x)$ is differentiable at $0$.
All other options involve $|x|$ in a way that makes the derivative discontinuous at $0$.
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