Consider the function $f(x) = \sin(x)$ over the interval $[\frac{-3\pi}{2}, \frac{\pi}{2}]$. State Rolle's Theorem and apply it to determine the guaranteed value(s) of c. Leave answers as exact values.
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Step 1: Rolle's Theorem states that if a function f(x) is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), and if f(a) = f(b), then there exists at least one number c in (a, b) such that f'(c) = 0. Show more…
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