Question

Mean Value Theorem:
Show that a polynomial of degree 3 has at most three real roots.

Answer 1

A similar example used Intermediate Theorem to prove that a root exists. I'm assuming I'm supposed to do the same here? Still, i don't have a solid grasp on Intermediate Theorem or what it even has to do with Mean Value Theorem.
Help?

Answer 2

Okay, do you know generally what the Mean Value Theorem is?

Answer 3

My overview of it is that it's a derivative parallel to the secant line between the two endpoints of a graph. And that somewhere between those two points this point of tangency exists so long as the graph is continuous and differentiable

Answer 4

That's the general idea. So assume that the domain is from negative infinity to infinity and you should know what a cubic root looks like in a graph

Answer 5

I'm imagining something like this with one secant line crossing at one point