BÀI TOÁN KHẢO SÁT HÀM SỐ BẬC BA TỔNG QUÁT CHẠY TRÊN PHẦN MỀM MAPLE

with(plots):with(student):
kshsb3:=proc(a,b,c,d)
local x,Y,dhbn,xct,A,B;
print(`Khao sat ham so bac ba`);
Y:=a*x^3+b*x^2+c*x+d;
print(`y=`,Y);
print(`Mien xac dinh cua ham so la R`);
print(`Khao sat chieu bien thien`); dhbn:=diff(Y,x);
print(`Dao ham bac nhat`); print(`dhbn=`,dhbn);
xct:=fsolve(dhbn=0);A:=solve(dhbn>=0);B:=solve(dhbn<=0);
if A=x then print(`Ham so dong bien tren toan truc so`);
print(`Ham so khong co cuc tri`);
print(`Gioi han cua ham so`);
print(Limit(Y,x=+infinity)=limit(Y,x=+infinity));
print(Limit(Y,x=-infinity)=limit(Y,x=-infinity));
print(`do thi ham so cat truc tung tai`);
print(intercept(y=Y,y=0,{x,y}));
print(`do thi ham so cat truc hoanh tai`);
print(intercept(y=Y,x=0,{x,y}));
print(plot(Y,x=-10..10,-10..10));
fi;
if B=x then print(`Ham so nghich bien tren toan truc so`);
print(`Ham so khong co cuc tri`);
print(`Gioi han cua ham so`);
print(Limit(Y,x=+infinity)=limit(Y,x=+infinity));
print(Limit(Y,x=-infinity)=limit(Y,x=-infinity));
print(`do thi ham so cat truc tung tai`);
print(intercept(y=Y,y=0,{x,y}));
print(`do thi ham so cat truc hoanh tai`);
print(intercept(y=Y,x=0,{x,y}));
print(plot(Y,x=-10..10,-10..10));
fi;
if A<>x then print(`Ham so dong bien tren cac khoang`);
print(solve(dhbn>=0,{x}));
print(`Ham so nghich bien tren cac khoang`);
print(solve(dhbn<0,{x}));
print(`Cac diem cuc tri cua ham so la`);
print(`Diem cuc dai`,intercept(y=Y,x=xct[1],{x,y}),`Diem cuc tieu`,intercept(y=Y,x=xct[2],{x,y}));
print(`Gioi han cua ham so`);
print(Limit(Y,x=+infinity)=limit(Y,x=+infinity));
print(Limit(Y,x=-infinity)=limit(Y,x=-infinity));
print(`do thi ham so cat truc tung tai`);
print(intercept(y=Y,y=0,{x,y}));
print(`do thi ham so cat truc hoanh tai`);
print(intercept(y=Y,x=0,{x,y}));
print(plot(Y,x=-10..10,-10..10));
fi;
end;