If $f(x) = \text{sgn}(x^3)$,then

Let $S = \{t \in R \mid f(x) = |x - \pi|(e^{|x|} - 1) \sin |x| \text{ is not differentiable at } t\}$. Then $S$ is

The number of critical points of the function $f(x) = \begin{cases} |\frac{\sin x}{x}|, & x \ne 0 \\ 1, & x = 0 \end{cases}$ in the interval $(-2\pi, 2\pi)$ is equal to:

Let $f: R \rightarrow R$ be a function defined by $f(x) = \max \{x, x^2\}$. Let $S$ denote the set of all points in $R$ where $f$ is not differentiable. Then $S$ is:

Which of the following statements is not true?

The set of all those points,where the function $f(x) = \frac{x}{1 + |x|}$ is differentiable,is