If Ax+By+Gz=D the equation of the tangent plane of the surface xy+yz+zx=3 at the point (1,1,1) then |A|+|B|+|G|=?
Any ideas how this prolem can be solved???
Hint: How do you calculate the derivatives with respect to a specific direction vector (think x, y, and z axes)? Given this what is the relationship to the tangent plane (i.e. how do you go from finding the partial derivatives for x,y,z at point (1,1,1) to tangent plane)?
Consider the surface given by z=f(xy). Let (x0y0z0) be any point on this surface. If f(xy) is differentiable at (x0y0), then the surface has a tangent plane at (x0y0z0). The equation of the tangent plane at (x0y0z0) is given by