Thread: Vector Tangent Line Problem

1. The problem statement, all variables and given/known data

Let f(x,y) = 5y^(2)-(2x^(2)+xy)

Then an implicit equation for the tangent plane to the graph of f at the point (0,-2) is




3. The attempt at a solution
I understand that I should take the derivative to find the gradient vector. For the derivative, I get <-4x-y,10y-x>.

I plug in (O,-2) and get <2,-20>.

My question is, what should I do to put this into implicit form??

Thanks!

Yes, you should take the gradient vector but you are taking the gradient of the wrong function. You want to take the gradient of the function F(x,y,z)= z- f(x,y)= z- 5y^2+ 2x^2+ xy= 0. The gradient of a function is always perpendicular to a "level curve" of the function.