Let $f(x) = |2x^2 + 5|x| - 3|$,$x \in R$. If $m$ and $n$ denote the number of points where $f$ is not continuous and not differentiable respectively,then $m + n$ is equal to:

If $f(x) = x(\sqrt{x} - \sqrt{x + 1}),$ then

If the function $f(x) = \begin{cases} \frac{(e^{kx}-1) \sin kx}{4 \tan x}, & x \neq 0 \\ P, & x=0 \end{cases}$ is differentiable at $x=0$, then

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

The number of points at which the function $f(x) = \max \{a-x, a+x, b\}$ for $-\infty < x < \infty$ and $0 < a < b$ is not differentiable, is

Let the function $f(x) = (x^2 - 1)|x^2 - ax + 2| + \cos|x|$ be non-differentiable at exactly two points $x = \alpha = 2$ and $x = \beta$. Then the distance of the point $(\alpha, \beta)$ from the line $12x + 5y + 10 = 0$ is equal to: