Re: Finding Tangent Plane

I know this is an old post, but it is what I am currently studying and I'm curious where the -1 value came from here.

Would anyone mind shedding some light on it for me?

Re: Finding Tangent Plane

Since the equation for the surface is $\displaystyle f(x,y,z) = g(x,y)-z = 0$, you can do a linear estimate:

$\displaystyle f(x,y,z)\approx{f}(x_0,y_0,z_0)+f_x(x_0,y_0,z_0)(x-x_0)+$

$\displaystyle f_y(x_0,y_0,z_0)(y-y_0)+f_z(x_0,y_0,z_0)(z-z_0)$,

which is the equation of the tangent plane. Of course $\displaystyle f_z$ is just -1 in this case.

- Hollywood