Concave and Convex Functions| Sydsaeter & Hammond 9.5, 9.6 | MME 1 Sem 1

Welcome to Lecture 36 of the online lecture series on Mathematical Methods in Economics I typically offered as a core paper to Eco(Hons.) Students in their first and second semester.

The textbook used in this video can be found here: https://drive.google.com/file/d/1eXtk...

We are referring to section 9.5, 9.6 on "Concave and Convex Functions" from the book by Knut Sydsaeter and Peter J. Hammond Mathematics for Economic Analysis

In this lecture, we discuss the following topics:
1. Graphs of Concave and Convex Functions
2. Testing for Concavity/Convexity: Second Derivative Test
3. Numerical Example : Second Derivative Test
4. Examples of Concave/Convex Functions in Economics
5. Composite Functions and Concavity/Convexity
6. What are Inflection Points?
7. Extreme Points & Concavity/Convexity
8. Jensen's Inequality
9. Strictly concave and convex functions
10. Numerical Example: Jensen's Inequality



For more videos on this lecture series:
1. Use of Logic in Maths:    • MME 1|LOGIC IN MATHS |NECESSARY & SUFFICIE...  
2. Methods to Prove any Mathematical Theorem:    • MME 1| Methods to Prove any MATHEMATICAL T...  
3. Functions of one variable:    • MME 1| Functions of one variable |Domain &...  
4. Graphs of Functions of 1 Variable:    • Graphs | Introduction to Co-ordinate Plane...  
5. Linear Functions:    • MME1 B.A.(H) Economics| Linear Functions| ...  
6. Quadratic Functions:    • MME 1|Quadratic functions| Quadratic Optim...  
7. Polynomials:    • MME 1|Polynomials| Remainder Theorem| Inte...  
8. Power & Exponential Functions:    • MME 1| Power Functions| Exponential Functi...  
9. Single Variable Differentiation:    • MME 1| Single Variable Differentiation| Ch...  
10 Rates of Change and their Economic Significance:    • MME 1|Rates of change & economic significa...  
11 Limits:    • MME 1| LIMITS | Sydsaeter & Hammond Ch 4 S...  
12. Rules of Differentiation:    • MME 1 |Rules of Differentiation|Differenti...  
14 Linear Approximations & Differentials:    • MME 1| Linear approximations & Differentia...  
15 Polynomial Approximation & Elasticity:    • Polynomial Approximation| Elasticity| Syds...  
16. Continuity:    • Continuity| Left Hand Limit| Right Hand Li...  
17 Differentiability:    • Differentiability| Left Hand Derivative & ...  
18 Infinite Sequence & Series:    • Geometric series| Infinite Sequence| Sydsa...  
19. Present Discounted Value & Investment Projects:    • Present Discounted Value| Investment Proje...  
20. Intermediate Value Theorem, Extreme Value Theorem & Mean Value Theorem:    • Intermediate value theorem| Extreme Value ...  
21. Taylor's Formula:    • Taylor's formula | Lagrange Remainder| App...  
22. L'hopital"s Rule:    • L'hopital"s Rule| Limits for Indeterminate...  
23 Inverse Functions:
24 Natural Exponential Function:    • The Natural Exponential Function| Sydsaete...  
25 Natural Logarithmic Function:    • Natural logarithmic function| Mathematical...  
26. Single Variable Optimization:    • Single variable Optimization| Finding Extr...  
27. Local Maxima and Minima:    • Local Maxima and Minima| Mathematical Econ...  
28 Concave and Convex Functions:    • Concave and Convex Functions| Sydsaeter & ...  

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