Newton's Method
Consider a sequence of x-values:
Begin with , chosen at pleasure.
Draw the tangent to the curve at x0:
The x-intercept of this tangent line, is the next number in the sequence:
Assuming f(x) has at least one real zero, under what conditions does it converge to a real zero of f(x)?
If I choose x0 blindly, the sequence can be grumpy. How can we help it along?