已知函数f(x)=x的平方+2x证明f(x)在[1,正无穷）上是减函数 求完整解题过程

f(x)=-x²+2x设 x1>x2≥1f(x1)-f(x2)=-x1²+2x1+x2²-2x2=-(x1²-x2²)+2(x1-x2)=-(x1-x2)(x1+x2)+2(x1-x2)=(x1-x2)[2-(x1+x2)]x1>x2≥1 x1-x2>0 x1+x2≥2 2-(x1+x2)≤0则 f(x1)-f(x2)