Calculus POD #11 Use the Intermediate Value Theorem to show that the equation has at least one solut

I give a brief mini-lecture about the IVT and then show you how it can be used to solve this problem:

Use the intermediate value theorem to show that the following equation has a solution on the given interval.

3x^3+x−1=0; (0,1)

Intermediate Value Theorem: If f is continuous on [a,b] and L is a number strictly between f(a) and f(b), then there exists at least one number c in (a,b) satisfying f(c) = L