# Product of Increasing Positive Functions is Increasing

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## Theorem

Let $f$ and $g$ be real functions defined on an interval $I$.

Let $f$ and $g$ be increasing and positive on $I$.

Then the product $f g$ is increasing on $I$.

## Proof

## Sources

- 2011: Robert G. Bartle and Donald R. Sherbert:
*Introduction to Real Analysis*(4th ed.) ... (previous): $\S 5.6$: Exercise $4$