Example 2: Example 2 (p. 678)

> f := y^2-x^2;

f := y^2-x^2

> g := x^2/4+y^2-1;

g := 1/4*x^2+y^2-1

>

> Pobj := plot3d( f, x=0..3, y=0..3 ):

> Pobj;

[Maple Plot]

> Pcon := implicitplot3d( g=0, x=0..2,y=0..2,z=0..5, color=cyan, style=patchnogrid ):

> Pcon;

[Maple Plot]

>

> display( Pobj, Pcon );

[Maple Plot]

>

> fx := diff( f, x );

> fy := diff( f, y );

fx := -2*x

fy := 2*y

> gx := diff( g, x );

> gy := diff( g, y );

gx := 1/2*x

gy := 2*y

>

> LE := fx=lambda*gx, fy=lambda*gy;

LE := -2*x = 1/2*lambda*x, 2*y = 2*lambda*y

> LEsol := solve( {LE,g=0}, {x,y,lambda} );

LEsol := {lambda = -4, x = 2, y = 0}, {lambda = -4,...

>

>

> sol := {seq( eval( [x,y], s ), s=LEsol )};

sol := {[2, 0], [-2, 0], [0, 1], [0, -1]}

>