Guys, please Help me. I give medals. Which one of the following statements is true? -If f ′′(x) > 0 on the interval (a, b) then f(x) is concave down on the interval (a, b). - If f ′(x) > 0 on the interval (a, b) then f(x) is increasing on the interval (a, b). -If f ′(c) = 0, then x = c is a relative maximum on the graph of f(x). -None of these are true.

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Guys, please Help me. I give medals. Which one of the following statements is true? -If f ′′(x) > 0 on the interval (a, b) then f(x) is concave down on the interval (a, b). - If f ′(x) > 0 on the interval (a, b) then f(x) is increasing on the interval (a, b). -If f ′(c) = 0, then x = c is a relative maximum on the graph of f(x). -None of these are true.

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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B is the answer. because c is wrong because if you have a slope of zero, it can be a max but it also can be a min. a is wrong because when you have concavity up, the f''x must be greater than zero and positive.
`If f ′(c) = 0, then x = c is a relative maximum on the graph of f(x)` there could be a relative min or a saddle point. So this statement is false.
`If f ′′(x) > 0 on the interval (a, b) then f(x) is concave down on the interval (a, b)` false. f(x) is concave up if the second derivative is positive
`If f ′(x) > 0 on the interval (a, b) then f(x) is increasing on the interval (a, b)` this is definitely true

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