I'm reading about tangent planes and have seen two different definitions. Is there a way to show they are equivalent?
At the very least is there a way to show that the second definition is equivalent to the plane (involving 2-dimensions)
$z = z_0 + f_x(x_0,y_0)(x-x_0) + f_y(x_0,y_0)(y-y_0)$ for which i presume the first definition is a generalisation, is that correct?