Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Mathematics LibreTexts

2: Differential Calculus of Functions of One Variable

( \newcommand{\kernel}{\mathrm{null}\,}\)

IN THIS CHAPTER we study the differential calculus of functions of one variable.

  • SECTION 2.1 introduces the concept of function and discusses arithmetic operations on functions, limits, one-sided limits, limits at ±, and monotonic functions.
  • SECTION 2.2 defines continuity and discusses removable discontinuities, composite functions, bounded functions, the intermediate value theorem, uniform continuity, and additional properties of monotonic functions.
  • SECTION 2.3 introduces the derivative and its geometric interpretation. Topics covered include the interchange of differentiation and arithmetic operations, the chain rule, one-sided derivatives, extreme values of a differentiable function, Rolle’s theorem, the intermediate value theorem for derivatives, and the mean value theorem and its consequences.
  • SECTION 2.4 presents a comprehensive discussion of L’Hospital’s rule.
  • SECTION 2.5 discusses the approximation of a function f by the Taylor polynomials of f and applies this result to locating local extrema of f. The section concludes with the extended mean value theorem, which implies Taylor’s theorem.


This page titled 2: Differential Calculus of Functions of One Variable is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by William F. Trench via source content that was edited to the style and standards of the LibreTexts platform.

Support Center

How can we help?