The number of points in the interval $(0,2)$ at which $f(x)=|x-0.5|+|x-1|+ an x$ is not differentiable is

Question

The number of points in the interval $(0,2)$ at which $f(x)=|x-0.5|+|x-1|+	an x$ is not differentiable is

Aicharya · Accepted Answer

Given, $f(x)=|x-0.5|+|x-1|+	an x$ Clearly $f(x)$ is not differentiable at $x=0.5,1$ and $\frac{\pi}{2}$ for $x \in(0,2)$. $	herefore$ Number of Non differentiable points of $f(x)$ are 3 . $	herefore$ Hence, option (c) is correct.

The number of points in the interval $(0,2)$ at which $f(x)=|x-0.5|+|x-1|+\tan x$ is not differentiable is

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