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After analyzing a function f(x), Edwin knew that f ′(3) = 0 and f ″(3) = −2. He therefore concluded that f(x) has an absolute maximum at x = 3. Edwina, his girlfriend, is not so sure. Explain why Edwina is unwilling to accept Edwin's conclusion. Homework Help ✎

Think about the definition of an absolute maximum, and the difference between that and a relative maximum.