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Mathematics, 18.08.2019 09:30 banks9244

If a function f is continuous for all x and if f has a relative maximum at (-1, 4) and a relative minimum at (3, -2), which of the following statements must be true?
(a) the graph of f has a point of inflection somewhere between x = -1 and x= 3
(b) f'(-1) = 0
(c) this is wrong
(d) the graph of f has a horizontal tangent line at x = 3
(e) the graph of f intersects both axes - correct answer
i understand why e is correct, but i do not get why a, b, and d are all wrong. aren't b and d to be expected since they are relative max/min's? i also can't imagine a case in which "a" is incorrect. can someone explain why they are wrong? you!

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