# Homework Help: F(x, y, z) = 0 f(x, y, z) =

1. Jul 3, 2010

### makyol

f(x, y, z) = 0 f(x, y, z) = ....

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Sorry have no idea:(

Last edited by a moderator: May 4, 2017
2. Jul 3, 2010

### HallsofIvy

Re: f(x, y, z) = 0 f(x, y, z) = ....

If a surface is given by f(x,y,z)= 0 (or any constant) we can think of it as a "level surface" so $\nabla f= f_x\vec{i}+ f_y\vec{j}+ f_z\vec{k}$ is normal to the surface. The tangent plane at $(x_0,y_0,z_0)$ is of the form $f_x(x_0,y_0,z_0)(x- x_0)+$$f_y(x_0,y_0,z_0)(y-y_0)+ f_z(x_0,y_0, z_0)(z- z_0)= 0$.

For what $(x_0, y_0, z_0)$ does (0, 0, 0) lie on that tangent plane?