anonymous
  • anonymous
Properties of cubics: Consider the general cubic polynomial f(x)=x^3+ax^2+bx+c, where a,b, and c are real numbers. a.Prove that f has exactly one local min. and one local max. provided that a^2>3b b. Prove that f has no extreme values if a^2<3b. c. Prove that for all real values of a,b,and c, the function has exactly one inflection point. Where is the inflection point located?
Mathematics
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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anonymous
  • anonymous
Properties of cubics: Consider the general cubic polynomial f(x)=x^3+ax^2+bx+c, where a,b, and c are real numbers. a.Prove that f has exactly one local min. and one local max. provided that a^2>3b b. Prove that f has no extreme values if a^2<3b. c. Prove that for all real values of a,b,and c, the function has exactly one inflection point. Where is the inflection point located?
Mathematics
schrodinger
  • schrodinger
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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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anonymous
  • anonymous
I got the answer of C, but im confused about part a and b :(

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