Newton's Method uses differentiation to solve non-linear equations and is especially useful when we can't factor the equation. It's very commonly used by computers when solving math-based problems.<\/p>\n
The graph allows you to explore 4 different functions, and to see what is going on when applying Newton's Method to those functions.<\/p>\n
You can see one of the big traps for the unwary. It doesn't always work out that the root you get is the closest one.<\/p>\n
For example, the initial guess in this case was x<\/i>0<\/sub> = 0.5. The closest root is near x<\/i> = 1.3, but the actual root found is one near x<\/i> = 2.<\/p>\n Also, strange things can happen if our first guess is too close to a local maximum or minimum. Try it!<\/p>\n I remember when I first learned Newton's Method. We happily differentiated and substituted. The examples were always \"nice\" with straightforward solutions. I wasn't really sure what was going on, even though I could apply the algorithm.<\/p>\n A visual representation is very useful for a better understanding of this concept.<\/p>\n See the 2 Comments<\/a> below.<\/p>\n","protected":false},"excerpt":{"rendered":"![\"Newton's](\"\/blog\/wp-content\/images\/2015\/07\/newton-example2.png\")
<\/a><\/p>\nVisuals are important<\/h2>\n
![\"Newton's](\"https:\/\/www.intmath.com\/blog\/wp-content\/images\/2015\/07\/newtons-method_th.png\")
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