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16 Differentiable functions[1C5]

Definition 32

[2D0]

To address the following exercises, it may be necessary to know some fundamental results in Analysis and Differential Calculus that may be found e.g. in [ 17 ] ; specifically:

Lagrange’s Theorem ¹ : Theorem 5.10 in in [ 17 ] , or [ .
De l’Hôpital’ rule, and corollaries: : Theorem 5.13 in in [ 17 ] , Sec. 7.12 in [ or [ ;
Taylor’s Theorem, and the possible remainders: Theorem 5.15 in in [ 17 ] , Chap. 7 in [ , or [ 59 ] .

E32: [1C6]
E32: [1C8]
E32: [1CB]
E32: [1CD]
E32: [1CG]
E32: [1CJ]
E32: [1CM]
E32: [1CP]
E32: [1CV]
E32: [1CX]
E32: [1CZ]
E32: [1D1]
E32: [1D4]
E32: [1D7]
E32: [1D9]

QuasiEsercizio 47

[1DB]

QuasiEsercizio 48

[1DC]

16.1 Higher derivatives

[2D1]

16.2 Taylor polynomial

[2D2]

16.3 Partial and total derivatives, differentials

[2D3]

16.4 Implicit function theorem

[2D4]

16.5 Constrained problems

[2D5]

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Authors: "Mennucci , Andrea C. G." .

Bibliography

[26] Walter Rudin. Principles of Mathematical Analysis. McGraw–Hill, New York, 3rd edition, 1964.
[6] T.M. Apostol. Calculus, Volume 1. Wiley, 1991. ISBN 9780471000051. URL https://books.google.it/books?id=o2D4DwAAQBAJ.
[26] Walter Rudin. Principles of Mathematical Analysis. McGraw–Hill, New York, 3rd edition, 1964.
[69] to3em. Mean value theorem — Wikipedia, the free encyclopedia. https://en.wikipedia.org/w/index.php?title=Mean_value_theorem&oldid=1164447679, 2023. [Online; accessed 16-September-2023].
[6] T.M. Apostol. Calculus, Volume 1. Wiley, 1991. ISBN 9780471000051. URL https://books.google.it/books?id=o2D4DwAAQBAJ.
[28] A. E. Taylor. L’Hospital’s rule. The American Mathematical Monthly, 59(1):20–24, 1952. ISSN 00029890, 19300972. URL http://www.jstor.org/stable/2307183.
[67] to3em. L’Hôpital’s rule — Wikipedia, the free encyclopedia, 2023. URL https://en.wikipedia.org/w/index.php?title=L'Hopital's_rule&oldid=1174053538. [Online; accessed 16-September-2023].
[74] to3em. Taylor’s theorem — Wikipedia, the free encyclopedia, 2023. URL https://en.wikipedia.org/w/index.php?title=Taylor's_theorem&oldid=1174353983. [Online; accessed 16-September-2023].

Book index

Lagrange's theorem
theorem, Lagrange's --- , see Lagrange's theorem
theorem, mean value --- , see Lagrange's theorem
mean value theorem , see Lagrange's theorem
Hospital , see Hôpital
theorem, Hôpital , see Hôpital rule
Hôpital rule
Taylor
Taylor's theorem
polynomial, Taylor's --- , see Taylor's theorem
expansion, Taylor's --- , see Taylor's theorem
formula, Taylor's --- , see Taylor's theorem
theorem, Taylor's --- , see Taylor's theorem
theorem, Taylor's ---, with Lagrange remainder , see Lagrange remainder

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