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Rolle's theorem applies to a function $f$ on $[a, b]$ if $f$ is:
AContinuous on $[a, b]$, differentiable on $(a, b)$, $f(a) = f(b)$
BJust continuous on $[a, b]$ at the chart endpoints here always
CJust differentiable on $(a, b)$ in the interior of the interval
DBounded on $[a, b]$ in the school chart with $f(a) = f(b)$
Answer & Solution
Correct answer: A. Continuous on $[a, b]$, differentiable on $(a, b)$, $f(a) = f(b)$
Rolle's: $f$ continuous on $[a, b]$, differentiable on $(a, b)$, $f(a) = f(b) \Rightarrow \exists c$ with $f'(c) = 0$.
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