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? Thank you!

(1) Answers

[latex]f'(x)=k(x+1)(x-3)[/latex] [latex]f'(x)=k(x^2-2x-3)[/latex] [latex]f(x)=k( \frac{x^3}{3}-x^2-3x )+C[/latex] [latex]f"(x)=k(2x-2)[/latex] if f"(x)=0 then x=1 therefore a) is true f'(-1)=0 b) is also true f'(3)=0 d) is also true  e) option is also correct i think

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