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Newton's Method for Solving a Quadratic Equation - Never Stop
I'm using Newton's Method to try to solve this equation:
$$
y = x^2 + 2x - 7
$$
where $x$ is the unknown.
As I understand it, Newton's Method will start with $x_0 = 7$ (or some other value close to the answer) and use the derivatives of the equation to calculate the next iteration of $x$:
$$
x_{n+1} = x_n - rac{f(x_n)}{f'(x_n)}
$$
After that, you keep repeating the process until either:
the value of $x$ is a root of the equation, or
the difference between the current value of $x$ and the last value of $x$ is smaller than some pre-determined threshold (I haven't gotten this far in class, so I'm not sure if this is even necessary).
If I understand correctly, the process ends when the derivative $f'(x_n)$ of $f(x) = x^2+2x-7$ is close to 0, which means that the second possibility is most likely what I should do.
I'm really struggling to get the code for it to work, however, because I can't figure out what to put into the derivative. Here is what I have so far:
for(x in 0:100){
for(y in 0:100){
if((x - y)^2 > 0){
tmp = (x - y)^2 ac619d1d87
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