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Math Help - Polynomial having a max/min on I

  1. #1
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    Polynomial having a max/min on I

    Without using derivatives, prove that a polynomial of even degree either has a maximum or a minimum on (-\infty,\infty). Give a simple criterion for deciding which it has.
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  2. #2
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    If the leading coefficient of the polynomial p(x) is positive then p(x) \rightarrow \infty as x \rightarrow \pm \infty. If said coefficient is negative p(x) \rightarrow -\infty. So with an argument similar to the one used here you can conclude that in the first case you have a minimum and in the second a maximum.
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