Question

For Rolle's Theorem to hold, the function f(x) must be continuous on the closed interval [a, b] and differentiable on (a, b). Which of the following is one of another necessary condition?

Answer 1

f(a) = f(b)

Answer 2

Rolle's Theorem requires three conditions: continuity on $[a, b]$, differentiability on $(a, b)$, and $f(a) = f(b)$. The first two are given in the question. The third, $f(a) = f(b)$, is the missing necessary condition.