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 .

The values of the derivative are always , and therefore it is for to have two or more real roots.

You can earn partial credit on this problem.