Trivial Inequality

The Inequality

The trivial inequality states that for all x. This is a rather useful inequality for proving that certain quantities are non-negative. The inequality appears to be obvious and unimportant, but it can be a very powerful problem solving technique.

Applications

Maximizing and minimizing quadratic functions

After Completing the square, the trivial inequality can be applied to determine the extrema of a quadratic function.

Instructive National Math Olympiad Problem

<Anyone want to dig one up?>