The greatest integer function $f(x) = [x]$ is differentiable for all values of
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $x ∈R-Z$
The greatest integer function $f(x)=[x]$ has jump discontinuities at every integer.
Hence it is:
• Not continuous at integers • Therefore not differentiable at integers
But it is continuous and differentiable for all non-integer real numbers.
So $f(x)$ is differentiable for all $x\in \mathbb{R}-\mathbb{Z}$.