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The function f(x) is defined as |[x]x| for 1<x2. The number of points where f(x) is non differentiable is 


Solution

f=|[x]x|=|[x]| |x| 

f(x)=⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪x,1<x<00,0x<1x,1x<24,x=2

L.H.L=limx1f(x)=0
R.H.L=limx1+f(x)=1
L.H.LR.H.L

L.H.L=limx2f(x)=2
R.H.L=limx2+f(x)=4
L.H.LR.H.L

f(x) discontinuous at x=1,2
Clearly, f(x) is not differentiable at x=1,2 and also ​​​​​​​f(x) is not differentiable at x=0

Hence, the number of points where f(x) is non differentiable is 3.
 

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