任取两点x1,x2且x1>x2≥1
f(x1)=-x1²+2x1
f(x2)=-x2²+2x2
f(x1)-f(x2)=-(x1²-x2²)+2(x1-x2)
=-(x1+x2-2)(x1-x2)<0
∴函数f(x)=-x²＋2x在[1,＋∞)上是减函数