Q1 of 64 Page 10

Choose the correct answer.

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


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.

More from this chapter

All 64 →
12

Write the value of the derivative of f(x) = |x – 1| + |x – 3| at x = 2.

 13

If write the value of

2

Choose the correct answer.

The function f(x) = sin–1(cos x) is


 3

Choose the correct answer.

The set of points where the function f(x) = x|x| is differentiable is