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Question

Let f:RR be a function defined by f(x)=max{x, x3}. Then the set of all points where f is not differentiable, is

A
{1,0}
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B
{1,0,1}
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C
{0,1}
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D
{1,1}
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Solution

The correct option is B {1,0,1}
f(x)={x,<x1 and 0x1x3,1<x<0 and x>1

At x=1,
LHD=1, RHD=3x2=3

At x=0,
LHD=3x2=0, RHD=1

At x=1,
LHD=1, RHD=3x2=3
Hence f is not differentiable at 1,0,1

Alternative solution :

Clearly, we can observe from the graph that the function f is not differentiable at x=1,0,1

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