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This chapter examines how derivatives are used to analyze function behavior and solve real-world problems. It covers monotonicity (increasing/decreasing functions), the identification of extrema (maxima/minima) via critical points, and the study of concavity and inflection points. Key mathematical principles discussed include the Mean Value Theorem, L’Hôpital’s Rule for limits, and the Newton-Raphson method for root-finding. Additionally, the chapter explores optimization—finding the most efficient dimensions or values in practical scenarios—and concludes with computational techniques using MATLAB for symbolic differentiation and solving equations.

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Applications of the Differentiation

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  • 发表日期：

    2026年

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  • Farzin Asadi

摘要

This chapter examines how derivatives are used to analyze function behavior and solve real-world problems. It covers monotonicity (increasing/decreasing functions), the identification of extrema (maxima/minima) via critical points, and the study of concavity and inflection points. Key mathematical principles discussed include the Mean Value Theorem, L’Hôpital’s Rule for limits, and the Newton-Raphson method for root-finding. Additionally, the chapter explores optimization—finding the most efficient dimensions or values in practical scenarios—and concludes with computational techniques using MATLAB for symbolic differentiation and solving equations.