Q. 15.0( 1 Vote )

# Choose the correct answer.Let f(x) = |x| and g(x) = |x3|, thenA. f(x) and g(x) both are continuous at x = 0B. f(x) and g(x) both are differentiable at x = 0C. f(x) is differentiable but g(x) is not differentiable at x = 0D. f(x) and g(x) both are not differentiable at x = 0

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.

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