Determine if Rolle's Theorem can be applied to the function $f(x) = \sin(x)$ on the closed interval $[\pi, 2\pi]$. If it can be applied, determine the value(s) of $c$ guaranteed by the theorem. If it cannot be applied, explain why.
Added by Albert H.
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Rolle's Theorem states that if a function $f(x)$ is continuous on the closed interval $[a, b]$, differentiable on the open interval $(a, b)$, and $f(a) = f(b)$, then there exists at least one value $c$ in $(a, b)$ such that $f'(c) = 0$. Show more…
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