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JEE Main 2007

Exam: JEE Main
Year: 2007
Subject: Mathematics
Chapter: Continuity and Differentiability

JEE Main 2007 · Mathematics · Continuity and Differentiability

Let f: R arrow R be a function defined by f(x)=Min\ x+1,|x|+1\ ....

Let

f: R \rightarrow R

be a function defined by

f(x)=\operatorname{Min}\{x+1,|x|+1\}

. Then which of the following is true? $Let f: R arrow R be a function defined by f(x)=Min\ x+1,|x|+1\ . Then which of the following is true?$

Options

A $f(x) \geq 1$ for all $x \in R$
B $f(x)$ is not differentiable at $x=1$
C $f(x)$ is differentiable everywhere
D $f(x)$ is not differentiable at $x=0$

Correct answer

C. $f(x)$ is differentiable everywhere

Step-by-step solution

f(x)=\min \{x+1,|x|+1\}

f(x)=x+1 \forall x \in R

. $Let f: R arrow R be a function defined by f(x)=Min\ x+1,|x|+1\ . Then which of the following is true?$

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