### COMP203: Lecture 23

Syllabus | Homework and Assignments | Grading Rubric | Midterm Exam | Final Project
Today we'll use Maple to write a program that uses Newton's method to search for the zeros (x-intercepts) of a function. You can find information on Newton's method in lectures 7 and 11 on Logo, on the internet, and in Maple. Maple already has a bulit-in tool for using Newton's method -- feel free to explore it, but don't use it in your program!

Your completed program should accept a function or expression and a guess at an x-intercept as inputs. It should output an "improved guess" at the x-intercept.

SAVE YOUR WORK OFTEN! It's not always possible to stop Maple when it gets into an infinite loop.

• It is strongly recommended that you test each step of your algorithm in Maple before trying to write a program.
• Do you want to work with functions or expressions? Each has advantages and drawbacks.
• How will you compute the derivative of your function or expression? The Maple function diff() may or may not be a good tool for this.
• What will you do with the derivative once you've found it? Note that the Maple command:
fprime := x -> diff(f(x),x);
probably doesn't do what you want it to.
• How will you evaluate the function/expression and its derivative at the guessed value?
• What will you do with the improved guess?
• How will you repeat the process to improve the guess?
• How will you stop your program when the guess is good enough?
• What inputs will your program need?
• What local and global variables will your program need?
• Should your output be in decimal or exact format?