If $f(x)=|x-3|$,then $f^{\prime}(3)$ is

If $f(x) = \begin{cases} k \cos x - x \cos k, & x \in [0, \frac{\pi}{2}] \\ k \sin x + x \sin k, & x \in (\frac{\pi}{2}, \pi] \end{cases}$ is differentiable in $(0, \pi)$,then:

Prove that the function $f$ given by $f(x) = |x - 1|, x \in R$ is not differentiable at $x = 1$.

If $f(x) = \begin{cases} \frac{1}{|x|} & ; |x| \geq 1 \\ ax^2 + b & ; |x| < 1 \end{cases}$ is differentiable at every point of the domain,then the values of $a$ and $b$ are respectively

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

The value of $m$ for which the function $f(x) = \begin{cases} mx^2, & x \le 1 \\ 2x, & x > 1 \end{cases}$ is differentiable at $x = 1$,is