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Limits Continuity and Differentiability question

2016 · Shift 0 · Q20

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PYQ Library
JEE Main
Mathematics
Limits Continuity and Differentiability
2016 · Shift 0 · Q20

Limits Continuity and Differentiability question

2016 · Shift 0 · Q20

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

For

x \in \,R,\,\,f\left( x \right) = \left| {\log 2 - \sin x} \right|\,\,

and

\,\,g\left( x \right) = f\left( {f\left( x \right)} \right),\,\,

then :

A
$g$ is not differentiable at $x=0$
B
$g'\left( 0 \right) = \cos \left( {\log 2} \right)$
C
$g'\left( 0 \right) = - \cos \left( {\log 2} \right)$
D
$g$ is differentiable at $x=0$ and $g'\left( 0 \right) = - \sin \left( {\log 2} \right)$

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