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  2. For business economics
  3. Chapter 5: Optimization
  4. Optimization convex/concave functions
  5. Functions of two variables
  6. Extrema and saddle points

Extrema and saddle points

Introduction: If a convex function has a stationary point, then we can immediately conclude that this stationary point is a minimum location of the function. Similarly, it follows that a stationary point of a concave function is a maximum location of the function.

Theorem:
  • A convex function has a minimum in a stationary point.
  • A concave function has a maximum in a stationary point.

Remark: A saddle point is a stationary point that is not a minimum or a maximum location of the function.
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Wiskunde Mathematics for business economics leeromgeving

 

  • Chapter 1: Functions of one variable
  • Chapter 2: Differentiation of functions of one variable
  • Chapter 3: Functions of two variables
  • Chapter 4: Differentiation of functions of two variables
  • Chapter 5: Optimization
    • Optimization functions of one variable
    • Applications 1
    • Optimization functions of two variables
    • Applications 2
    • Optimization constrained extremum problems
    • Applications 3
    • Optimization convex/concave functions
      • Functions of one variable
      • Functions of two variables
        • Convex and concave
        • Second-order condition
        • Extrema and saddle points
          • Example (film)
          • Exercise 1
          • Exercise 2
  • Chapter 6: Areas and integrals

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