Question

Give the point where |x|+|x+1| is differentiable

Answer 1

Answer:

repeat 90000000000000000000

Answer 2

Answer:

The short answer would be since |x||x| is not differentiable at x=0x=0 and |x−1||x−1| is not differentiable at x=1x=1, so f(x)f(x) will not be differentiable at x=0,1x=0,1 {Is it valid to claim this in every case ?}

Long answer:

f(x)=⎧⎩⎨1−2x12x−1 if x<0 if 0≤x<1 if x≥1f(x)={1−2x if x<01 if 0≤x<12x−1 if x≥1

limx→0+f(x)−f(0)x−0=limx→0+1−1x−0=0limx→0+f(x)−f(0)x−0=limx→0+1−1x−0=0

limx→0−f(x)−f(0)