 # Successive Approximations - Newton's Method

Videos and lessons with examples and solutions to help High School students explain why the x-coordinates of the points where the graphs of the equations y =f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

### Suggested Learning Targets

Explain why the intersection of y = f(x) and y = g(x) is the solution of f(x) = g(x) for any combination of linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Find the solution(s) by:
• Using technology to graph the equations and determine their point of intersection
• Using tables of values
• Using successive approximations that become closer and closer to the actual value.

Common Core: HSA-REI.D.11

Newton's Method
This video explains Newton's Method and provides an example. It also shows how to use the table feature of the graphing calculator to perform the calculations needed for Newton's Method.

Newton's Method
How to use Newton's Method to approximate a root.

Newton's Method - More Examples Part 1 of 3
How to use the Newton's Method formula to find two iterations of an approximation to a root.

Newton's Method - More Examples Part 2 of 3
How to use the Newton's Method formula to find two iterations of an approximation to a point of intersection of two functions.

Newton's Method - How it Can FAIL - More Examples Part 3 of 3
This video gives the geometric idea behind Newton's Method and show how it can go wrong and fail to yield an approximation. Newton's method does not always work.

Newton's Method Calculator

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.  