Choose the correct answer. Let f(x) = |x| and g(x) = |x 3 |, then

Question

Philoid · Accepted Answer

Given f(x) = |x| and g(x) = |x³|,

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.