If $f(x) = [x]$,where $[x]$ is the greatest integer not greater than $x$,then $f^{\prime}(1^{+}) = \dots$.

If $f(x) = \begin{cases} x^2 & \text{if } x \leqslant x_0 \\ ax + b & \text{if } x > x_0 \end{cases}$ is derivable for all $x \in \mathbb{R}$,then the values of $a$ and $b$ are respectively:

Let $f(x) = \begin{cases} (x - 1) \sin \frac{1}{x - 1}, & x \neq 1 \\ 0, & x = 1 \end{cases}$. Then which one of the following is true?

In the interval $[0, 3]$,the function $f(x) = |x - 1| + |x - 2|$ is

The set of all points where the function $f(x) = 2x|x|$ is differentiable 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: