If $f(x) = \begin{cases} x^2 + 3x + a, & x \leq 1 \\ bx + 2, & x > 1 \end{cases}$ is everywhere differentiable, then:

Let $f: R \rightarrow R$ be a function defined by $f(x)=\begin{cases} \frac{\sin(x^2)}{x} & \text{if } x \neq 0 \\ 0 & \text{if } x=0 \end{cases}$. Then,at $x=0$,$f$ is

If $f(x) = \begin{cases} x[x], & 0 \le x < 2 \\ (x-1)[x], & 2 \le x \le 4 \end{cases}$,where $[.]$ denotes the greatest integer function,then:

If $\alpha$ and $\beta$ are such that the function $f(x)$ defined by $f(x) = \begin{cases} \alpha x^2 - \beta, & |x| < 1 \\ \frac{-1}{|x|}, & |x| \ge 1 \end{cases}$ is differentiable everywhere,then the ordered pair $(\alpha, \beta) =$

The function $f(x) = a \sin |x| + b e^{|x|}$ is differentiable at $x = 0$ when

The function that is not differentiable at $x=1$ is