The greatest integer function defined by 𝒇(𝒙) = [𝒙], 𝟎 < 𝒙 < 𝟐 is not differentiable at x=_____.

1

Let’s draw the function f(x)=[x],

Let us check the continuity
f(x) at x=1 from the given interval.
We can see that function is not continuous,
Therefore, it will not be differentiable as well at x=1.