Limits Continuity And Differentiability Question 70
Question: The number of values of $ x\in [0,2] $ at which $ f(x)=| x-\frac{1}{2} |+| x-1 |+\tan x $ is not differentiable is
Options:
A) 0
B) 1
C) 3
D) none of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ | x-\frac{1}{2} | $ is continuous everywhere but not differentiable at $ x=\frac{1}{2} $ , $ | x-1 | $ is continuous everywhere but not differentiable at x=1, and tan x is continuous in [0, 2] except at $ x=\frac{\pi }{2} $ .
Hence, $ f(x) $ is not differentiable at $ x=\frac{1}{2},1,\frac{\pi }{2}. $
BETA
