$f(x) = |\log_e |x||$ is differentiable at

If $f(x) = \begin{cases} x + 1, & x < 2 \\ 2x - 1, & x \ge 2 \end{cases}$,then $f'(2)$ equals

The function $f(x) = (x^2 - 1)|x^2 - 3x + 2| + \cos(|x|)$ is not differentiable at

If the function $g(x) = \begin{cases} ae^x, & x \le 0 \\ b\cos x + x, & x > 0 \end{cases}$ is differentiable,then the value of $a^2 + b^2$ is

If $f(x)=\begin{cases} \frac{2 x e^{\frac{1}{2 x}}-3 x e^{\frac{-1}{2 x}}}{e^{\frac{1}{2 x}}+4 e^{\frac{-1}{2 x}}} & \text{if } x \neq 0 \\ 0 & \text{if } x=0 \end{cases}$ is a real valued function,then:

Define a function $f: R \rightarrow R$ by $f(x) = \begin{cases} \frac{\sin x^2}{x}, & \text{for } x < 0 \\ x^2 + ax + b, & \text{for } x \geq 0 \end{cases}$. Suppose $f(x)$ is differentiable on $R$. Then,