Limits Continuity And Differentiability Question 54
Question: Let $ f:R\to R $ be a function defined by $ f(x)=min{x+1,| x |+1} $ , Then which of the following is true?
Options:
A) $ f(x) $ is differentiable everywhere
B) $ f(x) $ is not differentiable at x = 0
C) $ f(x)\ge 1 $ for all $ x\in R $
D) $ f(x) $ is not differentiable at $ x=1 $
Show Answer
Answer:
Correct Answer: A
Solution:
$ f(x)=\min {x+1,| x |+1} $
$ \Rightarrow f(x)=x+1\forall x\in R $
Hence, $ f(x) $ is differentiable everywhere for all $ x\in R $ .
BETA
