Why would you pick Newtons method over differentiation?
If you are given a option to use one of them to solve a problem. Which would you pick? Is there certain problems where one is more beneficial?

Question

Why would you pick Newtons method over differentiation?
If you are given a option to use one of them to solve a problem. Which would you pick? Is there certain problems where one is more beneficial?

kinggeorge · Answer

The main purpose of newton's method is to approximate the roots. There are quite a few polynomials where we can not express the roots in exact form, and Newton's method would be very helpful in these cases.

anonymous · Answer

roots in exact form meaning? they are imaginary unless newtons method is applied?

kinggeorge · Answer

In exact form such as the roots of $-3x^2-5x+23$. You can find these using the quadratic formula. Your roots would be $$x=\frac{5\pm\sqrt{25+276}}{-6}$$

However, if you look at the polynomial $x^5-3x-1$, it is impossible to find the exact form of any real roots. In this case, Newton's method would let you find very good approximations.

anonymous · Answer

Ahhhhh I see, Cheers mate. Thanks a lot

kinggeorge · Answer

You're welcome.