The following activity will introduce you to Newton's Method, showing you an example on a specific function, and letting you formulate the algorithm to perform Newton's Method.

Spend a minute just playing with the app, what everything does and how it works.In this example, our initial guess at the root of the function is [math]x_0=1.6[/math] for the function [math]f\left(x\right)=\frac{1}{2}x^2+x+1-e^x[/math].[br][br]Hit the reset button, and push the next button until the point [math]x_1[/math] appears. Then, continue until [math]x_2[/math] appears, and repeat a few times. [br][br][b]Question 1: [/b]Given one of the points [math]x_i[/math], explain how the next point [math]x_{i+1}[/math] is found in words. You can write it as a list of steps.[br][br][b]Question 2: [/b]Next, we want to write this algorithm as an equation. Using mathematical notation, if we know the value of [math]x_i[/math], what will the recursive formula for [math]x_{i+1}[/math] be?[br]