AP EAMCET20227 Jul 2022Morning ShiftMathematicsContinuity and DifferentiabilityActual

Which of the following is differentiable at x=0 ?

Options

Af(x)= |x|+|x|
Bf(x)= |x|+|x|
Cf(x)= |x|-|x|
Df(x)= |x|-|x|

Correct answer

D. f(x)= |x|-|x|

Step-by-step solution

At x=0 , RHD |x|-|x|= _ h 0 ( |h|-|h|-(0) h aligned & = _ h 0 ( h h -1 ) & =1-1=0 aligned LHD of |x|-|x|= _ h 0 ( |-h|-|-h|) -h =0 aligned & = _ h 0 [ ( h -h )+1 ] & =0 aligned L H D=R H D |x|-|x| is differentiable at x=0

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