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

The left-hand derivative of $f(x) = [x]\sin(\pi x)$ at $x = k$,where $k$ is an integer and $[x]$ denotes the greatest integer function $\le x$,is:

Let $f : (-1, 1) \to \mathbb{R}$ be a function defined by $f(x) = \min\{-|x|, -\sqrt{1 - x^2}\}$. If $K$ is the set of all points at which $f$ is not differentiable,then $K$ has exactly

The function $g(x) = \begin{cases} x + b, & x < 0 \\ \cos x, & x \geqslant 0 \end{cases}$ can be made differentiable at $x = 0$.

Define $f(x) = \begin{cases} x^2 + bx + c, & x < 1 \\ x, & x \geq 1 \end{cases}$. If $f(x)$ is differentiable at $x = 1$,then $(b - c)$ is equal to

Identify the correct statement about the function $f(x) = \max(x^2 - 1, 7 - x^2, 5)$.