The greatest integer function $f(x) = [x]$ is defined as the greatest integer less than or equal to $x$. This function is constant between any two consecutive integers but has jump discontinuities at every integer value.
For the interval $0 < x < 3$, the function $f(x) = [x]$ is discontinuous at the integer values $x = 1$ and $x = 2$. Since a function must be continuous at a point to be differentiable there, the function is definitely not differentiable at $x = 1$ and $x = 2$.
At any non-integer point $c$ in the interval $(0, 3)$, the function is locally constant (i.e., $f(x) = [c]$ for $x$ in a small neighborhood around $c$). Since the derivative of a constant is zero, the function is differentiable at all non-integer points. At the integer points $x = 1$ and $x = 2$, the left-hand limit and right-hand limit do not coincide, confirming non-differentiability.
Final Answer: At only two points
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