Limits Continuity And Differentiability Question 75
If $ f(x)= \begin{cases} x^{3},\ x^{2}<1 \ x,\ x^{2}>1 \end{cases} . $ , then $ f(x) $ is differentiable at
Options:
A) $ (-\infty ,\infty )-{1} $
B) $ (-\infty ,\infty )\tilde{\ }{1,-1} $
C) $ (-\infty ,\infty )\setminus{1,-1,0} $
D) $ (-\infty ,\infty )\tilde{\ }{-1} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ f(x) $ is clearly continuous for $ x\in \mathbb{R} $ . $ f’(x) $ is non-differentiable at $ x=1,-1. $
$ f’(x)= \begin{cases} 3x^{2},,x^{2}<1 \ 1,,x^{2}>1 \ \end{cases} .$
Thus, f(x) is non-differentiable at $ x=1,-1 $
BETA
