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:

If $f(x) = \begin{cases} e^x + ax, & x < 0 \\ b(x - 1)^2, & x \ge 0 \end{cases}$ is differentiable at $x = 0$,then $(a, b)$ is

Let $f(x) = \begin{cases} (x - 1) \sin \frac{1}{x - 1}, & x \neq 1 \\ 0, & x = 1 \end{cases}$. Then which one of the following is true?

Let $R$ denote the set of all real numbers. Define the function $f: R \rightarrow R$ by $f(x) = \begin{cases} 2-2x^2-x^2 \sin \frac{1}{x} & \text{if } x \neq 0 \\ 2 & \text{if } x=0 \end{cases}$. Then which one of the following statements is True?

If the function $g(x) = \begin{cases} k\sqrt{x+1}, & 0 \le x \le 3 \\ mx + 2, & 3 < x \le 5 \end{cases}$ is differentiable,then the value of $k+m$ is:

The function given by $y = ||x| - 1|$ is differentiable for all real numbers except the points