# Tangent Plane

• September 26th 2008, 04:03 PM
Aryth
Tangent Plane
Find the equation for the plane tangent to the surface z = f(x,y) at the indicated point:

$z = x^3 + y^3 - 6xy, (1,2,-3)$

I get stuck at finding the third component of the gradient of z.
• September 26th 2008, 05:34 PM
Jhevon
Quote:

Originally Posted by Aryth
Find the equation for the plane tangent to the surface z = f(x,y) at the indicated point:

$z = x^3 + y^3 - 6xy, (1,2,-3)$

I get stuck at finding the third component of the gradient of z.

the tangent plane to a curve $z = f(x,y)$ at a point $(x_0,y_0,z_0)$ is given by

$z - z_0 = f_x(x_0,y_0)(x - x_0) + f_y(x_0,y_0)(y - y_0)$