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Section: Differentiable Functions
Many properties of real-valued functions are reflected by their derivatives. Thus, the study of differentiation of real-valued functions helps to better understand the following:
* The occurrence of their local minima or maxima (see example),
* Their monotonic behavior (see example),
* Their convexity (see example).
Moreover, the growth and fluctuations of the functions can be estimated by boundaries of their derivatives (see example).
Table of Contents
- Definition: Difference Quotient
- Definition: Derivative, Differentiable Functions
- Definition: Higher-Order Derivatives
- Definition: Local Extremum
- Theorem: Rolle's Theorem
- Proposition: Differentiable Functions and Tangent-Linear Approximation
- Proposition: Characterization of Monotonic Functions via Derivatives
- Theorem: Darboux's Theorem
- Proposition: Basis Arithmetic Operations Involving Differentiable Functions, Product Rule, Quotient Rule
- Proposition: Chain Rule
Thank you to the contributors under CC BY-SA 4.0!
- Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983