1
Question
If f(x)=|x+1|(|x|+|x−1|) then at what points the function is/are not differentiable at in the interval [−2,2]
If f(x)=|x+1|(|x|+|x−1|) then at what points the function is/are not differentiable at in the interval [−2,2]
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Solution
The correct options are
A −1
B 1
D 0
f(x)=⎧⎪
⎪
⎪⎨⎪
⎪
⎪⎩(x+1)(2x−1),−2≤x<−1(x+1)(1−2x),−1≤x<0x+1,0≤x<1(x+1)(2x−1),1≤x≤2
Since the function is continuous at all points,
f′(x)=⎧⎪
⎪⎨⎪
⎪⎩4x+1,−2≤x<−1−4x−1,−1≤x<01,0≤x<14x+1,1≤x≤2
Function is not differentiable at x=−1,0,1
A −1
B 1
D 0
f(x)=⎧⎪ ⎪ ⎪⎨⎪ ⎪ ⎪⎩(x+1)(2x−1),−2≤x<−1(x+1)(1−2x),−1≤x<0x+1,0≤x<1(x+1)(2x−1),1≤x≤2
Since the function is continuous at all points,
f′(x)=⎧⎪ ⎪⎨⎪ ⎪⎩4x+1,−2≤x<−1−4x−1,−1≤x<01,0≤x<14x+1,1≤x≤2
Function is not differentiable at x=−1,0,1
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