Q. 15.0( 1 Vote )

# Choose the correct answer.

Let f(x) = |x| and g(x) = |x^{3}|, then

A. f(x) and g(x) both are continuous at x = 0

B. f(x) and g(x) both are differentiable at x = 0

C. f(x) is differentiable but g(x) is not differentiable at x = 0

D. f(x) and g(x) both are not differentiable at x = 0

Answer :

Given f(x) = |x| and g(x) = |x^{3}|,

Checking differentiability and continuity,

LHL at x =0,

RHL at x =0,

And f(0)=0

Hence, f(x) is continuous at x =0.

LHD at x =0,

RHD at x =0,

∵ LHD ≠RHD

∴ f(x) is not differentiable at x =0.

Checking differentiability and continuity,

LHL at x =0,

RHL at x =0,

And g(0)=0

Hence, g(x) is continuous at x =0.

LHD at x =0,

RHD at x =0,

∵ LHD = RHD

∴ g(x) is differentiable at x =0.

Hence, option A is correct.

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