A) {-1, 1}
B) {-1, 0}
C) {0, 1}
D) {-1, 0, 1}
Correct Answer: D
Solution :
[d] \[f(x)=\max .\,\,\left\{ x,{{x}^{3}} \right\}\] \[=\left\{ \begin{matrix} x; & x<-1 \\ {{x}^{3}}; & -1\le x\le 0 \\ x; & 0\le x\le 1 \\ {{x}^{3}}; & x\ge 1 \\ \end{matrix} \right.\] \[\therefore f'(x)=\left\{ \begin{matrix} 1; & x<-1 \\ 3{{x}^{2}}; & -1\le x\le 0 \\ 1; & 0\le x\le 1 \\ 3{{x}^{2}}; & x\ge 1 \\ \end{matrix} \right.\] Clearly f is not differentiable at -1, 0 and 1.
You need to login to perform this action.
You will be redirected in
3 sec
