Newton-Raphson method with two x values

1. Nov 6, 2005

LakeMountD

Find the value of x1 and x2 that minimize the function f= x1^2 + x2^2 + 10x1 +20x2 +25 . This isn't that difficult of a problem if there was only 1 x value. But how do I do it when it is using x1 and x2?

2. Nov 6, 2005

LakeMountD

Okay I think I might have figured something out. I split the problem up to be f(x1)=x1^2+10x1+5 and f(x2)=x2^2+20x2+25 and then do newton-raphson for each of those functions. Is this correct?

3. Nov 6, 2005

NateTG

In this case, it's going to pretty easy since there aren't any terms in the expression for $f(x_1,x_2)$ that involve both $x_1$ and $x_2$ so you can indeed do this one by finding the minimums with respect to $x_1$ and $x_2$.