MATH.10:9 - Consequences

A constrained comparison becomes a reusable calculation. It can expose a feasible improvement, reduce an optimization problem to a condition or explain why a proposed change cannot help.

The main effort is constructing a useful admissible family and establishing the sign over the range needed by the conclusion. The Method permits an early useful result; full optimization is a larger task when the working question demands it. Keeping the family and argument makes later changes of criterion or constraints easier to handle.