How would i solve this? f(x) = x^3+ax^2 + bx +c a. over what interval f concave up? concave down? b. show that f must have exactly one flection point. c. given the (0,-2) is the inflection point of f, compute a and c and then show that f has no critical point

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How would i solve this? f(x) = x^3+ax^2 + bx +c a. over what interval f concave up? concave down? b. show that f must have exactly one flection point. c. given the (0,-2) is the inflection point of f, compute a and c and then show that f has no critical point

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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it is concave up when the second derivative is positive and concave down when the second derivative is negative inflection points are where the second derivative crosses the x-axis so since the second derivative is always increasing it only does this once use the fact that the second derivative is 0 at inflection points to solve for a and then plug in x = 0 and y = -2 into the original equation to solve for c

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