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

with(plots):with(student):
kshsb4:=proc(a,b,c,d,e)
local x,Y,dhbn,xct,A,B,dhbh;
print(`Khao sat ham so bac bon`);
Y:=a*x^4+b*x^3+c*x^2+d*x+e;
print(`y=`,Y);
print(`Tap xac dinh cua ham so la R`);
print(`Khao sat chieu bien thien`); dhbn:=simplify(diff(Y,x));
print(`Dao ham bac nhat`); print(`dhbn=`,dhbn);dhbh:=diff(dhbn,x);
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}));
xct:=fsolve(dhbn=0);A:=solve(dhbh<0);B:=solve(dhbh>0);
if (a<0 and A=x) or (a>0 and B=x) then print(`Cac diem cuc tri cua ham so la`);
print(intercept(y=Y,x=xct,{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=-5..5,-5..5,colour=blue));
fi;
if (A<>x)and (B<>x)
then print(`Cac diem cuc tri cua ham so la`);
print(intercept(y=Y,x=xct[1],{x,y}));print(intercept(y=Y,x=xct[2],{x,y}));
print(intercept(y=Y,x=xct[3],{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=-5..5,-5..5,colour=blue));
fi;
end: