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Section: Differentiable Functions
Many properties of realvalued functions are reflected by their derivatives. Thus, the study of differentiation of realvalued 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: HigherOrder Derivatives
 Definition: Local Extremum
 Theorem: Rolle's Theorem
 Proposition: Differentiable Functions and TangentLinear 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
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References
Bibliography
 Forster Otto: "Analysis 1, Differential und Integralrechnung einer VerĂ¤nderlichen", Vieweg Studium, 1983