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Question

The set of all those points, where the function

f(x)=x1+|x|

is differentiable, is



A

(,)

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B

[0, ]

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C

(,0)(0,)

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D

(0,)

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Solution

The correct option is B

(,)


Let h(x)=x,xϵ(,);g(x)=1+|x|,xϵ(,)
Here h is differentiable in (,) but |x| is not differentiable at x=0.
Therefore g is differentiable in (,0)(0,) and g(x)0,x(,).

f(x)=h(x)g(x)=x1+|x|
It is differentiable in (,0)(0,) for x = 0
limh0f(h)f(0)h0=limh0h1+|h|h=limh011+|h|=1
Therefore f is differentiable at x = 0, so f is differentiable in (,).


Mathematics

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