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Let f:RtoR be a function defined by f(x)...

Let `f:RtoR` be a function defined by `f(x)="min"{x+1,|x|+1}`. Then which one of the following is true?

A

`f(x) gt 1"for all " x in R`

B

`f(x)"is not differentiable at x=1"`

C

`f(x)"is everywhere differentiable"`

D

`f(x)"is not differentiable at x=0"`

Text Solution

Verified by Experts

The correct Answer is:
C
It is evident from the graphs of y=x+1 and `y=|x|+1"that "f(x)=min [x+1,|x|+1=x+1"for all "x in R`. Clearly, f(x)=x+1 is everywhere differentiable. ,
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