In this problem you will use Rolle's theorem to determine whether
it is possible for the function
to have two or more real roots (or, equivalently, whether the graph of
crosses the -axis two or more times).

Suppose that has at least two real roots. Choose
two of these roots and call the smaller one and the
larger one . By applying Rolle's theorem to on the
interval , there exists at least one number
in the interval so that .