Putra Pratama's page

> restart;
> with(plots):
Warning, the name changecoords has been redefined

> Elips:=[9*cos(theta),7*sin(theta),0]:
> f:=(x,y)->x+2*y+30;

> Dasar:=spacecurve(Elips,theta=0..2*Pi,color=red):
> Tujuan:=plot3d(f,-9..9,-7..7):
> Pilihan:=(axes=frame,orientation=[150,40],labels=[x,y,z]):
> display({Dasar,Tujuan},Pilihan);

> Proyeksi:=spacecurve([Elips[1],Elips[2],f(Elips[1],Elips[2])],theta=0..2*Pi,color=red,thickness=3):
> display({Dasar,Tujuan,Proyeksi},Pilihan);

> F:=f(Elips[1],Elips[2]);

> plot(F,theta=0..2*Pi);

> Dif_F:=diff(F,theta);

> TKritis:=solve(Dif_F=0,theta);

> NMaks:=simplify(subs(theta=TKritis,F));

> NMaksElips=simplify(subs(theta=TKritis,Elips));

> LevelCurve:=plot3d(f,-9..9,-7..7,style=contour,axes=normal,contours=20,orientation=[270,0]):
> display({LevelCurve,Dasar},axes=normal);

> Level:=solve(f(x,y)=a,y);

> [f(-9,-7),f(-9,7),f(-9,-7)];

> animate({[Elips[1],Elips[2],theta=0..2*Pi],[x,Level,x=-9..9]},a=7..53,scaling=constrained,frames=32);

> CartElips:=x^2/81+y^2/49=1;

> CartElips_1:=subs(y=y(x),CartElips);

> TurunanImp:=diff(CartElips_1,x);

> Turunan:=solve(TurunanImp,diff(y(x),x));

> Kemiringan:=subs(y(x)=y,Turunan);

> solve({CartElips,Kemiringan=-1/2},{x,y});

> Solusi:=allvalues(%);

> eks1:=subs(Solusi[1],f(x,y));

> eks2:=subs(Solusi[2],f(x,y));

> f1:=(x,y)->(x-2)^2+(y+1)^2:
> levelcurve:=plot3d(f1,-9..9,-7..7,style=contour,axes=normal,contours=20,orientation=[270,0]):
> display({levelcurve,Dasar},axes=normal);

> {Diff(f1(x,y),x)=0,Diff(f1(x,y),y)=0};

> tls0:=value(%);

> htls0:=solve(tls0,{x,y});

> subs(%,f1(x,y));

> g1:=(x,y)->x^2/81+y^2/49:
> with(linalg):
Warning, the protected names norm and trace have been redefined and unprotected

> dg1:=grad(g1(x,y),[x,y]);

> df1:=grad(f1(x,y),[x,y]);

> persamaan:={df1[1]=lambda*dg1[1],df1[2]=lambda*dg1[2],g1(x,y)=1};

> tkrit:=solve(persamaan,{x,y,lambda});

> tk:=evalf(allvalues(tkrit));

> [f1(-8.991993504,.976528417),f1(4.06563197,-6.2450585477)];

>