I see in a book that under the following condition newton-raphson method (for finding the zero of a function) converges:
1) The function is continuously differentiable
2) The function is positive in the left side of the root and negative in the right side of the root
3) The derivative of the function is negative and bounded in a neighbourhood of the root.
4) The initial guess is in a small neighbourhood of the root.
I want to know a proof for that.