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Question

If f(x)=|x+1|(|x|+|x1|) then at what points the function is/are not differentiable at in the interval [2,2]

A
1
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B
0
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C
1
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D
1/2
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Solution

The correct options are
A 1
B 1
D 0
f(x)=⎪ ⎪ ⎪⎪ ⎪ ⎪(x+1)(2x1),2x<1(x+1)(12x),1x<0x+1,0x<1(x+1)(2x1),1x2
Since the function is continuous at all points,
f(x)=⎪ ⎪⎪ ⎪4x+1,2x<14x1,1x<01,0x<14x+1,1x2
Function is not differentiable at x=1,0,1

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