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Math Help - Prove the maximum number of critical points.

  1. #1
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    Prove the maximum number of critical points.

    Let f(x) be a polynomial of degree n.

    (a) What is the maximum number of critical points f(x) can have? For each n, give an example, with proof, of a polynomial having the maximum number for that n.

    (b) Answer the same question with "maximum" replaced with "minimum."
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  2. #2
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    Quote Originally Posted by cgiulz View Post
    Let f(x) be a polynomial of degree n.

    (a) What is the maximum number of critical points f(x) can have? For each n, give an example, with proof, of a polynomial having the maximum number for that n.

    (b) Answer the same question with "maximum" replaced with "minimum."

    A critical point of a function is where its first derivative vanishes, so...

    Tonio
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