A function is defined on as , where denotes the greatest integer .
The number of points, where is not differentiable in is __________ .
The explanation for the answer:
Step 1: Checking the points of the function
The function is
The limit is .
So we need to check the points
We know that, if a function is continuous in the point, then it will be differentiable at that point.
Now we are going to check the continuity of the function at these points.
Step 2: Finding continuity of the function at
(a) Take
(b) Take ,
(c) Take ,
Step 3: Finding continuity of the function at
(d) Take
(e) Take
Thus the function is not continuous at .
Hence, the number of points, where f is not differentiable in is points.