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

If $f(x) = \begin{cases} A + Bx^2, & x < 1 \\ 3Ax - B + 2, & x \geqslant 1 \end{cases}$,then find $A$ and $B$ so that $f(x)$ is differentiable at $x = 1$.

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,

Let $f(x)=a_0+a_1|x|+a_2|x|^2+a_3|x|^3$,where $a_0, a_1, a_2, a_3$ are real constants. Then $f(x)$ is differentiable at $x=0$ if and only if:

The function $y = \sin^{-1}(\cos x)$ is not differentiable at . . . . . .

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