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Question

Let f(x)={max{|x|,x2},|x|282|x|,2<|x|4
Let S be the set of points in the interval (4,4) at which f is not differentiable. Then S :
  1. is an empty set
  2. equals {2,1,1,2}
  3. equals {2,1,0,1,2}
  4. equals {2,2}


Solution

The correct option is C equals {2,1,0,1,2}
For |x|2

f(x)=x2,2x1|x|,1<x<1x2,1x2
Therefore ,
For x[4,4]

f(x)=⎪ ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪ ⎪8+2x,4x<2x2,2x1|x|,1<x<1x2,1x282x,2<x4

f is not differentiable at x{2,1,0,1,2}
S={2,1,0,1,2}

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