Applications of Differential Calculus to Limit Calculations and Extremum Problems

E. Mahmudov ()
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E. Mahmudov: Istanbul Technical University

Chapter Chapter 7 in Single Variable Differential and Integral Calculus, 2013, pp 185-221 from Springer

Abstract: Abstract Certain kinds of limit computations, those involving the so-called indeterminate forms, can be accomplished using two rules explained in this chapter, L’Hopital’s rule and a rule based on the Taylor–Maclaurin series. Again, studying the Taylor series around critical points gives sufficient conditions for the presence of a local (relative) extremum. Furthermore, whether the curve is bending (upward or downward) depends on the sign of higher order derivatives. Necessary and sufficient conditions for existence of an asymptote to a curve are proved. Finally, such investigations are used in curve sketching.

Keywords: Global Minimum; Tangent Line; Global Maximum; Selling Price; Differential Calculus (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-91216-86-2_7

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DOI: 10.2991/978-94-91216-86-2_7

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