15.4 Geometric significance of partial derivatives

Problem 80, page 942. The paraboloid z= intersects the plane x=1 in a parabola.

find the parametric equations for the tangent line to this parabola at the point (1,2,-4).

> with(plots): F:=plot3d([1,y,z],y=-3..4,z=-10..6,style=wireframe,color=yellow,numpoints=4000): P:=plot3d([x,y,15-3*x-8*y],x=-2..1,y=-0..4,style=wireframe,color=blue,numpoints=5500): G:=plot3d([x,y,6-x-x^2-2*y^2],x=-2..1,y=-2..4,style=wireframe,color=black,numpoints=400): display(F,G,P,axes=frame,labels=[x,y,z]);