What you’ll learn to do: Explain Newton’s Method as an iterative process to approximate

In many areas of pure and applied mathematics, we are interested in finding solutions to an equation of the form [latex]f(x)=0[/latex]. For most functions, however, it is difficult—if not impossible—to calculate their zeroes explicitly. In this section, we take a look at a technique that provides a very efficient way of approximating the zeroes of functions. This technique makes use of tangent line approximations and is behind the method used often by calculators and computers to find zeroes.