Let $f(x)=\left\{\begin{matrix}(x-2)^2\sin\left(\frac{1}{x-2}\right)-|x|&,&x≠2\\-2&,&x=2\end{matrix}\right.$ then the points where f (x) is not differentiable are
Answer & explanation
Correct answer: option 2
$f'(2)=\underset{h→0}{\lim}\frac{h^2\sin\frac{1}{h}-(2+h)+2}{h}$
Since $(x-2)^2\sin\left(\frac{1}{x-2}\right)$ is differentiable at x = 0
and |x| is not differentiable at x = 0
∴ f (x) is not differentiable at x = 0