Product of Increasing Positive Functions is Increasing

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

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Sources

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