WebFeb 3, 2024 · Informally, Rolle’s theorem says that if the outputs of a differentiable function f are equal at the end positions of an interval, then there should be an internal point c where \(f’(c) = 0\). Other than being beneficial in determining the mean-value theorem, Rolle’s theorem is sometimes used, as it builds only the existence of a solution ... WebApr 22, 2024 · Example 2: Verify Rolle’s theorem for the function f ( x) = – x 2 + 5 x – 5 on a closed interval [ 1, 4]. Solution: The function is a simple polynomial function, so it is continuous in the interval [ 1, 4], and it is differentiable in the interval ( 1, 4). Let us verify the third condition f ( a) = f ( b).
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