► My Applications of Derivatives course: https://www.kristakingmath.com/applications-of-derivatives-course
Newton's method is a tool you can use to estimate the root of a function, which is the point at which the function crosses the x-axis.
The only tricky part about using Newton's method is picking a starting value. The starting value is like your first estimate for the root, and the closer the starting value is to the actual root, the fewer the iterations of Newton's method you'll have to do. Sometimes it'll be easy to pick a starting value, because you'll be given an interval in which to look for the root, and you can just pick the midpoint of the interval.
If you're not given a closed interval, then you'll want to try to guess where the root might be, and pick a starting value close to that. If you don't have any guess, you can always just pick a starting value of 0.
Once you have the starting value, you'll plug it into the Newton's method formula. You have to always use the previous result of the Newton's method formula to get the next estimate, and you keep applying the formula over and over until you get the estimate to repeat the same value to a certain number of decimals.
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com
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Tagged under: interval,calculus,derivatives,educational,estimate,calculus expert,newton' method,decimal places,root,estimation,expert,Krista King,
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