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).

  1. Definition: Difference Quotient
  2. Definition: Derivative, Differentiable Functions
  3. Definition: Higher-Order Derivatives
  4. Definition: Local Extremum
  5. Theorem: Rolle's Theorem
  6. Proposition: Differentiable Functions and Tangent-Linear Approximation
  7. Proposition: Characterization of Monotonic Functions via Derivatives
  8. Theorem: Darboux's Theorem
  9. Proposition: Basis Arithmetic Operations Involving Differentiable Functions, Product Rule, Quotient Rule
  10. Proposition: Chain Rule

Branches: 1

Thank you to the contributors under CC BY-SA 4.0!




  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983