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Limits Continuity and Differentiability question

2007 · Shift 0 · Q41

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JEE Main
Mathematics
Limits Continuity and Differentiability
2007 · Shift 0 · Q41

Limits Continuity and Differentiability question

2007 · Shift 0 · Q41

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Let

f:R \to R

be a function defined by

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

, then which of the following is true?

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

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