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Question

Let f(x)={2,3x0x2,x<x3 and g(x)=f(|x|)+|f(x)|
Which of the following statements is/are correct?
1. g(x) is differentiable at x=0.
2. g(x) is differentiable at x=2.
Select the correct answer using the code given below

A
1 only
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B
2 only
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C
Both 1 and 2
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D
Neither 1 nor 2
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Solution

The correct option is C 1 only
Given : f(x)={2,3x0x2,0<x3

g(x)=f(|x|)+|f(x)|




By the given f(x),the graph of f|x|and|f(x)| are shown in the graph.

If we add both f(|x|)and|f(x)|

g(x)=f|x|+|f(x)|




Since at x=2 ,the graph is sharp point.Hence it is not differentiable at x=2

Therefore at x=0 according to the graph, it is differentiable.

Therefore option A is the correct answer.

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