Limits Continuity And Differentiability Question 84
Question: Let $ f:R\to R $ be a function defined by f(x) max $ {x,x^{3}} $ . The set of all points where f(x) is NOT differentiable is
Options:
A) {-1, 1}
B) {-1, 0}
C) {0, 1}
D) {-1, 0, 1}
Show Answer
Answer:
Correct Answer: D
Solution:
$ f(x)=\max .{ x,x^{3} } $
$ = \begin{vmatrix} x; & x<-1 \\ x^{3}; & -1\le x\le 0 \\ x; & 0\le x\le 1 \\ x^{3}; & x\ge 1 \\ \end{vmatrix} . $
$ \therefore f’(x)= \begin{vmatrix} 1; & x<-1 \\ 3x^{2}; & -1\le x\le 0 \\ 1; & 0\le x\le 1 \\ 3x^{2}; & x\ge 1 \\ \end{vmatrix} . $ Clearly f is not differentiable at -1, 0 and 1.
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