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

Let $[x]$ denote the greatest integer function and $f(x) = \begin{cases} 4x^2 + [2x]x, & \text{if } x \in [-\frac{1}{2}, 0) \\ ax^2 - bx, & \text{if } x \in [0, \frac{1}{2}) \end{cases}$. Then:

The number of points in the interval $(0,2)$ at which $f(x)=|x-0.5|+|x-1|+\tan x$ is not differentiable is

$f(x) = \begin{cases} [\cos \pi x]; & x \leqslant 1 \\ 2\{x\} - 1; & x > 1 \end{cases}$ Comment on the derivability at $x = 1$,where $[\cdot]$ denotes the greatest integer function and $\{\cdot\}$ denotes the fractional part function.

If $f(x) = \operatorname{Max} \{3 - x, 3 + x, 6\}$ is not differentiable at $x = a$ and $x = b$,then $|a| + |b| =$

Let $g: [-2, 2] \rightarrow R$ and $f: [-2, 2] \rightarrow R$ be two functions defined as $g(x) = \begin{cases} -1, & \text{if } -2 \le x < 0 \\ x^2 - 1, & \text{if } 0 \le x \le 2 \end{cases}$ and $f(x) = |g(x)| + g(|x|) + 2$. In the interval $(-2, 2)$, $f$ is not differentiable at $x = $