4) In lecture we discussed the graphical intuition behinds Newton's method for finding the root of some function f(x). Given an iterate Pn, the next iterate comes from finding the root of the function L(x), where L is the tangent to f(x) at the point x = Pn. What is L(x)? From your answer to (a), find the root L(x) and show that it reproduces the formula for Newton's method.