Give an equation of the tangent plane to the paraboloid $z = x^2 +y^2$ at a point $(x_0, y_0, x^2_0 + y^2_0)$
I think I am on the right track but one thing confuses me. First I find the partial derivatives with respect to $x $ and $y$.
$Fx(a,b) = 2x$
$Fy(a,b) = 2y$
I plug in the values...
$Fx(x_0, y_0) = 2x_0$
$Fy(x_0, y_0) = 2y_0$
Now I am confused. I do not know what to do with $z$. This is a 3rd order function, am I supposed to find the partial derivative of $z$ as well?
I know I am supposed to plug in these values...
$z = 2x_0(x-x_0) + 2y_0(y-y_0)$
But I do not know what to do with $z$. I've never worked with 3rd order functions. Can someone clear this up for me?