wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

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

Open in App
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.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon