The function $f(x) = \begin{cases} e^x + ax, & x < 0 \\ b(x - 1)^2, & x \geq 0 \end{cases}$ is differentiable at $x = 0$. Then

If $f(x) = |x - 3|,$ then $f$ is

$A$ function $f$ is defined on $[-3,3]$ as
$f(x) = \begin{cases} \min \{|x|, 2-x^{2}\} & , -2 \leq x \leq 2 \\ [|x|] & , 2 < |x| \leq 3 \end{cases}$
where $[x]$ denotes the greatest integer $\leq x$. The number of points,where $f$ is not differentiable in $(-3,3)$ is

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

Let $f(x) = \begin{cases} \sin x, & \text{for } x \ge 0 \\ 1 - \cos x, & \text{for } x \le 0 \end{cases}$ and $g(x) = e^x$. Then $(g \circ f)'(0)$ is

Let $f:[-1,1] \rightarrow R$ be a function defined by $f(x)=\begin{cases} x^2 \left| \cos \left(\frac{\pi}{x}\right) \right| & \text{for } x \neq 0 \\ 0 & \text{for } x=0 \end{cases}$. The set of points where $f$ is not differentiable is