设f(x1) f(x2) 1> x2>x1 >0
f(x2)-f(x1)
=x2/(x2-1)-x1/(x1-1)
=x2*(x1-1)-x1*(x2-1)/(x2-1)(x1-1)
=x1-x2/(x2-1)(x1-1)
因为 1> x2>x1 >0
所以 x1-x20
x1-x2/(x2-1)(x1-1) x2>x1 >0
f(x2)-f(x1)
=x2/(x2-1)-x1/(x1-1)
=x2*(x1-1)-x1*(x2-1)/(x2-1)(x1-1)
=x1-x2/(x2-1)(x1-1)
因为 1> x2>x1 >0
所以 x1-x20
x1-x2/(x2-1)(x1-1)