Application of Differential Calculus to Rate Problems in Real-World Systems

Mathematics — 2025, Undergraduate

This study applied differential calculus to rate and optimisation problems drawn from real-world systems. Representative problems involving rates of change, related rates, and extreme values were formulated and solved analytically, with results interpreted in context. The findings revealed that calculus-based methods determined optimal and critical points accurately, while sensitivity to parameter changes was tractable through derivatives. The study observed improved problem interpretation when solutions were checked against physical context. It recommends embedding application-based problems in calculus instruction.

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