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[All Steps] Let I:=[a, b] and let f: I \rightarrow R be continuous on I. If f has an absolute maximum [respectively, minimum] at an interior point c of

Question: Let \(I:=[a, b]\) and let \(f: I \rightarrow \mathbb{R}\) be continuous on \(I\). If \(f\) has an absolute maximum [respectively, minimum] at an interior point \(c\) of \(I\), show that \(f\) is not injective on \(I\).

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