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point c
Rolle's Theorem states that for a differentiable function f, if the outputs at the endpoints of an interval are equal, there exists an interior point [point c|point c] where f'(c) = 0.
Definition
Rolle's Theorem states that for a differentiable function f, if the outputs at the endpoints of an interval are equal, there exists an interior point point c where f'(c) = 0.
Mechanism
point c By the Mean <a href='/en/entity/value-theorem'>Value Theorem</a>, there exists a point c ∈ (0, 5/3) where s'(c) = -40 ft/sec, satisfying the theorem's requirement. This follows from Rolle's theorem through a constructed function that meets its criteria.
Effects
point c As a result, the absolute maximum must occur at an interior point c € (a, b).