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anonymous
 5 years ago
Why does a function being well defines and it having a point c where lim_x>c{((f(x)f(c))/(xc)^2}=A < 0 guarantee that f'(c) exists and that c is a maximum point?
anonymous
 5 years ago
Why does a function being well defines and it having a point c where lim_x>c{((f(x)f(c))/(xc)^2}=A < 0 guarantee that f'(c) exists and that c is a maximum point?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I believe I understand the 2nd part of it. Since the bottom of the limit is positive at all times, and the result is negative, that means that f(x)f(c) is negative on both sides of the limit and use that to prove that f(c) is a maximum point. What I'm really stuck on is proving differentiability. I'll repost the limit with symbols:\[\lim_{x \rightarrow c}(f(x)f(c))/(xc)^2 = A < 0\]
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