Proof: let f (x) = x 2-x.

f '(x)= 2x- 1 >； 0

So f(x) increases monotonically at 1 when x>.

So f(x)>f( 1)=0,

That is, the proof of inequality.

This is just to illustrate a method. Using derivative to prove inequality, we can draw a conclusion by constructing a function and then proving monotonicity.