Abstract
We now begin the differential calculus for real valued functions of several variables. The first step is to define the notions of directional derivative and partial derivative. Then the concept of differentiable function is introduced, by linear approximation to the increments of a function. Taylor’s formula with remainder is obtained for functions of class C(q); such functions have continuous partial derivatives of orders 1, 2,..., q. It is then applied to problems of relative extrema and to the characterization of convex functions of class C(2).
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© 1977 Springer-Verlag, New York Inc.
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Fleming, W. (1977). Differentiation of real valued functions. In: Functions of Several Variables. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9461-7_3
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DOI: https://doi.org/10.1007/978-1-4684-9461-7_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-9463-1
Online ISBN: 978-1-4684-9461-7
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