Question

find the equation of the plane tangent to the surface:
3x^2 + 2y^2 +z^3 = 29 at the point: (1,-3,2)

Answer 1

first make sure ... it touches the surface.
Then take gradient
\[ \nabla(3x^2 + 2y^2 +z^3) = <6x, 4y, 3z^2> = values\; of\; x,y,z\]

There you have your normal component of plane.
now you only need to find the remainding component d of ax+by+cz+d= 0 which you can do by ... putting values of x,y,z

Answer 2

perfect thanks!