Around 1948, Kantorovich published his famous results on Newton's method. His results assert that if a function belongs to a specific class and satisfies a set of conditions at a given point, then within a certain radius, there exists a (sometimes unique) root of the function. Moreover, when Newton's method is initiated at that point, it converges quadratically to the root. The uses Newton's method to prove the existence of the root. We will prove the existence of the root without using any algorithm, instead using variational principles. Then, we will extend his work by considering other classes of functions.