Exercício 4.14

> f:=x->(1-x)/(x^2+1);
X:=vector(3,[1/4.,1/2.,3/4.]);
fX:= vector(3,[f(X[1]),f(X[2]),f(X[3])]);
poli:=PoliNewton(X,fX,10);
p:=x->poli:
A:=pointplot({[X[1],fX[1]],[X[2],fX[2]],[X[3],fX[3]]},axes=BOXED):
B:=plot(p(x),x=1./4..3/4.):
C:=plot(f(x),x=1./4..3/4,color=blue):
display({A,B,C});
plot(f(x),x=0..2,color=blue);

> X:=vector(5,[-1,-1/2.,0.,1/2.,1.]);
fX:= vector(5,[f(X[1]),f(X[2]),f(X[3]),f(X[4]),f(X[5])]);
poli:=PoliNewton(X,fX,10);
p:=x->poli:
A:=pointplot({[X[1],fX[1]],[X[2],fX[2]],[X[3],fX[3]],[X[5],fX[5]],[X[5],fX[5]]},axes=BOXED):
B:=plot(p(x),x=X[1]..X[5],color=red):
C:=plot(f(x),x=X[1]..X[5],color=blue):
display({A,B,C});