Q. 15.0( 1 Vote )

Choose the correct answer.

Let f(x) = |x| and g(x) = |x3|, 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) = |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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