In-Class Work:
d:=[ [41,38], [63,56], [70,59], [72,64], [84,74]];
f:=(41*a+b-38)^2+(63*a+b-56)^2+(70*a+b-59)^2+(72*a+b-64)^2+(84*a+b-74)^2;
solve({diff(f,a)=0,diff(f,b)=0});
p1:=plot(d,style=point,symbolsize=10,symbol=circle,color=blue):
L:= x -> 417*x/505+1869/505;
p2:=plot(L(x),x=41..84):
display(p1,p2);
L(69);
evalf(%);
Surface for #2:
f:= (x,y) -> 4*x*y-x^3-2*y^2;
p1:=plot3d(f(x,y), x=-2..2, y=-2..2, style=patchnogrid, axes=boxed):
p2:=implicitplot3d(x^2+y^2+z^2=.01, x=-.1.. .1, y=-.1.. .1, z=-.1.. .1, color=violet, style=patchnogrid):
p3:=implicitplot3d((x-4/3)^2+(y-4/3)^2+(z-f(4/3,4/3))^2=.01, x=4/3-.1..4/3+.1, y=4/3-.1.. 4/3+.1, z=f(4/3,4/3)-.1..f(4/3,4/3)+.1, color=red, style=patchnogrid):
display(p1,p2,p3);