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Lecture# Derivatives and Extrema: Theory and Applications

Description

This lecture covers the theory of derivatives, including the calculation of derivatives for various functions such as trigonometric functions, polynomials, and composite functions. The instructor discusses the concept of local extrema and the conditions for a function to have a local maximum or minimum. The lecture also explores the application of derivatives in finding maximum and minimum points of functions on closed intervals, using the Mean Value Theorem and Rolle's Theorem. Additionally, the lecture delves into hyperbolic functions, their derivatives, and the concept of hyperbolic tangents and cotangents. The importance of finding critical points and verifying extremum points is emphasized through theoretical explanations and practical examples.

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In course

Instructor

MATH-101(e): Analysis I

Étudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles d'une variable.

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In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic on the whole complex plane. Typical examples of entire functions are polynomials and the exponential function, and any finite sums, products and compositions of these, such as the trigonometric functions sine and cosine and their hyperbolic counterparts sinh and cosh, as well as derivatives and integrals of entire functions such as the error function.

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Hyperbolic functions

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