Question

Let $f\left(x\right)=\left\{\begin{matrix} max \left\{\left|x\right| , x^{2}\right\} & \left|x\right|\leq 3 \\ 12-\left|x\right| & \, \, 3 < \left|x\right|\leq 12 . \end{matrix}\right$ If $S$ is the set of points in the interval $\left(- 12 , 12\right)$ at which $f$ is not differentiable, then $S$ is

• A. equal to $\left\{- 3 , 3\right\}$
• B. equal to $\left\{- 3 , - 1 , 1 , 3\right\}$
• C. an empty set
• D. equal to $\left\{- 3 , - 1 , 0 , 1 , 3\right\}$

Answer 1

Answer: (D)

Here, $f(x)=\left\{\begin{array}{cc}12+x & -12 \leq x < -3 \\ x^{2} & -3 \leq x \leq-1 \\ |x| & -1 < x < 1 \\ x^{2} & 1 \leq x \leq 3 \\ 12-x & 3 < x \leq 12\end{array}\right.$

Hence, $f\left(x\right)$ is not differentiable at $x=-3,-1,0,1,3$
$\Rightarrow S=\left\{- 3 , - 1 , 0 , 1 , 3\right\}$