Show that the cubic $\displaystyle p(x) = x^3 + ax^2 + bx + c $ has extreme values iff $\displaystyle a^2 > 3b. $
Any cubic goes from -infinityto +infinity. The extreme values occur when there is a bump, i.e., the derivative is zero. When you take the derivative, you'll get a quadratic. If it has real roots, you've found where the bumps are. The quadratic formula should help you.