1. ## Tangent Plane

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

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

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

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

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

I get stuck at finding the third component of the gradient of z.
the tangent plane to a curve $\displaystyle z = f(x,y)$ at a point $\displaystyle (x_0,y_0,z_0)$ is given by

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