JEE Main2012MathematicsContinuity and DifferentiabilityActual

If f(x)=a| x|+b e^ |x| +c|x|^3 , where a, b, c R , is differentiable at x=0 , then

Options

Aa=0, b and c are any real numbers
Bc=0, a=0, b is any real number
Cb=0, c=0, a is any real number
Da=0, b=0, c is any real number

Correct answer

D. a=0, b=0, c is any real number

Step-by-step solution

| x| and e^ |x| are not differentiable at x=0 and |x|^3 is differentiable at x=0 . for f(x) to be differentiable at x=0 , we must have a=0, b=0 and c is any real number.

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