jee-main 2007 Q104

jee-main · India Curve Sketching Continuity and Differentiability of Special Functions

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?
(1) $f ( x ) \geq 1$ for all $x \in R$
(2) $f ( x )$ is not differentiable at $x = 1$
(3) $f ( x )$ is differentiable everywhere
(4) $f ( x )$ is not differentiable at $x = 0$

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?\\
(1) $f ( x ) \geq 1$ for all $x \in R$\\
(2) $f ( x )$ is not differentiable at $x = 1$\\
(3) $f ( x )$ is differentiable everywhere\\
(4) $f ( x )$ is not differentiable at $x = 0$

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