# Newton's method

## Main Question or Discussion Point

lets say i have the functions f(x,y) = cos(x-y) - y and g(x,y) = sin(x+y) - x. I want to use newton's method to approximate these functions. Do I just take the partial derivatives with respect to x and y of each function and plug in a given point (a,b)?

EnumaElish
Homework Helper
Do you mean to approximate the roots? Or do you mean to approximate an extremum (min or max)?

HallsofIvy
Homework Helper
As EnumaElish said, you don't use Newton's method to "approximate" functions- you use Newton's method to find approximate (numerical) solutions to equations. What really is the problem?

Both, I am not sure how to use it for one and for the other. And yes I meant approximate solutions, I assumed it was just semantics but obviously it isnt.

HallsofIvy
The tangent plane to z= f(x,y) at $(x_0, y_0)$, is
$$z= f_x(x_0,y_0)(x- x_0)+ f_y(x_0,y_0)(y- y_0)$$