Project 6 Due 9 October

Use Maple to do the following ten problems
1. #73 in 12.3 hint ?diff
2. #77 in 12.3
3&4 #6 in 12.6 hint with(linalg): g:=(x,y)->grad(x^2*y^3,[x,y]);

Use Maple find all the critical points and classify as local min, local max or
saddle points. You should plot the functions too, but do not turn in
the plots.

hint here is a maple solution to #7
readlib(unassign);
unassign('x','y');
f:=(x,y)->4*x^2+y^2 -4*x+2*y;
critical:=solve({diff(f(x,y),x)=0,diff(f(x,y),y)=0});
Delta:=unapply((diff(f(x,y),x,x)*diff(f(x,y),y,y) - (diff(f(x,y),x,y))^2),x,y);
unassign('x','y');assign(critical[1]);Delta(x,y);
unassign('x','y');assign(critical[2]);Delta(x,y);
___OR___
for i from 1 to nops([critical])
do
	unassign('x','y');
	critical[i];
	assign(critical[i]);
	Delta(x,y);
od

#5,6, 7, 8 are problems in section 12.7 numbers 6, 7, 8 and 12

#9, 10 is #1 on 12.8