Most Important Selected Qs for JEE AdvancedMathematicsContinuity and Differentiability

f(x)= (|x|+[x]) , then

Options

Af is continuous at x=1 / 2
Bf is continuous at x=0
Cf is differentiable in (-1,0)
Df is differentiable in (0,1)

Correct answer

D. f is differentiable in (0,1)

Step-by-step solution

aligned & f(x)= (|x|+[x]) & f(0)=1, f(0-0)= (-1)=-1 & f(1 / 2)= ( 1 2 )=0, f ( 1 2 -0 )= ( 1 2 )=0 & f ( 1 2 +0 )= 2 =0 & for x (0,1) f(x)= x & for x (-1,0) f(x)= (-x-1)=- x aligned

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