Multivariate Calculus: multivariate calculus - #27254

Question:

(a)	Part of a landscape generated in a computer game is defined by the quadric surface \[z=3{{x}^{2}}+2xy+{{y}^{2}}+10x+2y+5\].
	(i)	Obtain the critical point of the surface and determine if it is a maximum, a minimum or a saddle point.
	(ii)	Determine the equation of the tangent plane to the surface at the point where \[x=-1\] and \[y=0\].
	(iii)	Find or state a vector that is parallel to the normal to the surface where \[x=-1\] and \[y=0\].	[11]
(b)	(i)	Construct the bilinear surface patch based on the line segments joining \[A\left( 1,\,1,\,0 \right)\] with \[B\left( 2,\,1,\,1 \right)\] and \[C\left( 1,\,2,\,0 \right)\] with \[D\left( 2,\,2,\,0 \right)\].
	(ii)	Obtain the parametric equations of the curve joining A to D.
	(iii)	Show that the curve joining B to C is a parabola lying in the plane \[x+y=3\].	[9]

Multivariate Calculus: multivariate calculus – #27254