Abstract
In this chapter we develop the basic theory of derivatives of real-valued functions of one variable. The geometric motivation of the derivative of f at c is that it is the limit of the slope of lines joining (c, f(c)) to nearby points on the graph of f, as these points approach c, and therefore represents the slope of a “line passing through two consecutive points” of the graph of f, i.e., the tangent line. We can enjoy such language without succumbing to it.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer Science+Business Media New York
About this chapter
Cite this chapter
Browder, A. (1996). Differentiation. In: Mathematical Analysis. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0715-3_4
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0715-3_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6879-6
Online ISBN: 978-1-4612-0715-3
eBook Packages: Springer Book Archive