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Mathematics for Economists
Chapter 9
Functions of several variables
Functions of two variables
Graph of a function of two variables
Functions of several variables
Functions of several variables: Problems
Problem: Evaluate a function of two variables
Problem: Evaluate a function of two variables
Problem: Find the natural domain of a function of two variables
Problem: Level curves
Problem: Intersection of level curves
Partial derivatives
Partial derivatives, rough introduction
Partial derivatives
Hessian
Chain rule for functions of two variables
Partial derivatives: Problems
Problem: Find partial derivatives
Problem: Find partial derivatives
Problem: Find first- and second-order partial derivatives
Problem: Find first- and second-order partial derivatives
Problem: Find first- and second-order partial derivatives
Problem: Hessian and its determinant
Problem: Concave function of two variables
Problem: Chain rule
Problem: Chain rule
Problem: Chain rule
Problem: Chain rule
Problem: Slope of a level curve
Problem: Slope of a level curve
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Chapter 9
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Problem: Hessian and its determinant
Problem
Find the Hessian for the following function
f
(
x
,
y
)
=
x
2
−
2
y
2
−
3
x
y
−
4
x
+
2
Find the determinant of the Hessian
Show solution
Solution
H
=
(
)
|
H
|
=
−
8
−
9
=
−
17
.