Newton's method? Test Tomorrow!!?

Question

I was wondering if someone could tell me a general overview of Newton's metod and how it relates to Calculus and Derivatives? What is the difference between Newton's method and the Bisection method? I'm trying to review for a test tomorrow but having trouble finding the difference and what Newton's method is about.....

Thanks..

Answer 1

newton's method

write it over and over and drill on simple problems till you fall asleep and write as much as you can on the test for partial credit and maybe you will learn it by than

Answer 2

The NR method uses the slope (the first derivative) at some point close to a root and extrapolates back to the x-axis to get closer to that root. Remember that the first derivative is the change in y (dy) divided by the change in x (dx). So NR takes the guessed x-value and calculates the y value at that guessed x. The y-value (function value) is divided it by dy/dx. This gives a dx value (a correction) that should be subtracted from the guess for the next x guess. Say the guess is 5 (doesn't matter what the equation is in this example), the function value (f(5)) is 10, and the derivative (dy/dx) is 2. The derivatve at that point means that y changes 2 units for every unit of x. So the function has a value of 10 and the new value of X should be corrected by 5 units (10/2 = 5), That is, if you drew the slope and extrapolated to the x-axis, it would intersect 5 units from the x-value guess. So the new guess is the last one less 5. That is how it works.

Answer 3

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