Newton-Raphson method with two x values

[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?

 

[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?

 

[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.