Just a question regarding Rolle's Theorem that I can't really find an explanation to. (Below)

Question

mendicant_bias · Answer

"The function
$$f(x) = [1] --- x, 0 \le x <1$$$$f(x) = [2] --- 0, x = 1$$
is zero at x = 0and x = 1 and differentiable on (0,1), but its derivative on (0,1) is never zero. How can this be? Doesn't Rolle's Theorem say the derivative has to be zero somewhere in (0,1)? Give reasons for your answer."

sirm3d · Answer

rolle's theorem requires that the function must be continuous on the closed interval $$0\leq x \leq 1$$, which is not satisfied by your function