# Math Help - Polynomial having a max/min on I

1. ## 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.

2. 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.