What is the Tangent Plane at a Given Point on a Level Surface?

[makyol]

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

Homework Statement

[PLAIN]http://www.netbookolik.com/wp-content/uploads/2010/07/q12.png

Homework Equations

The Attempt at a Solution

Sorry have no idea:(

 

[HallsofIvy]

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?