Question give the surface $x^2$ $=$ $y(2+3x+z)$ and ask me to proof that there is a point on that surface that is not in any tangent planes of the surface
I put the graph in Wolfram Alpha and get that there is a double elliptical cone with one pointy-like point
I think that point is the answer with the same idea of 2D graph with a sudden twist having no tangent line
also, I did partial differentiation depending on each variable and get:
if I consider tangent plane formula of:
$f_x(x-a)+f_y(y-b)+f_z(z-c) = 0$
can I find the point by letting $f_x,f_y,f_z$ all equal to $0$ and conclude that the point that satisfies this condition be my point not being in any tangent plane
And can this be the proof?