Derivatives and Their Applications

Steen Pedersen ()
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Steen Pedersen: Wright State University, Department of Mathematics

Chapter 6 in From Calculus to Analysis, 2015, pp 91-126 from Springer

Abstract: Abstract Local properties algebra derivatives and the relationship between the sign of the derivative at a point and the function being monotone at a point. Global properties of the derivative include Rolle’s Theorem, the Mean Value Theorem (MVT), and Darboux’s Theorem. Applications include Taylor polynomials, l’Hopital’s rule, Liouville’s theorem about transcendental numbers, and some aspects of convex function theory.

Keywords: Lipschitz Condition; Local Extremum; Mean Value Theorem; Taylor Polynomial; Transcendental Number (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-13641-7_6

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