Chapter 12: Q. 21 (page 988)

Give precise mathematical definitions or descriptions of each of the following concepts that follow. Then illustrate the definition with a graph or an algebraic example.
A function $f (x, y)$ has a saddle point at a point $(x_{0}, y_{0})$ .

Short Answer

Expert verified

A point $(x_{0}, y_{0})$ in the domain of a function $f (x, y)$ is called a saddle point of $f$ if $(x_{0}, y_{0})$

is a stationary point of $f$ at which there is neither a maximum nor a minimum.

Step by step solution

Step 1. Given information

A function $f (x, y)$ has a saddle point at a point $(x_{0}, y_{0})$ .

Step 2. Defining saddle point

A point $(x_{0}, y_{0})$ in the domain of a function $f (x, y)$ is called a saddle point of $f$ if $(x_{0}, y_{0})$

is a stationary point of $f$ at which there is neither a maximum nor a minimum.

A saddle point for a function, $g (x, y) = x^{2} - y^{2}$ , is shown below.

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Give precise mathematical definitions or descriptions of each of the following concepts that follow. Then illustrate the definition with a graph or an algebraic example.
A function $f (x, y)$ has a saddle point at a point $(x_{0}, y_{0})$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Defining saddle point

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Give precise mathematical definitions or descriptions of each of the following concepts that follow. Then illustrate the definition with a graph or an algebraic example.A function f(x,y) has a saddle point at a pointx0,y0.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Defining saddle point

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Geometry

Statistics

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Give precise mathematical definitions or descriptions of each of the following concepts that follow. Then illustrate the definition with a graph or an algebraic example.
A function $f (x, y)$ has a saddle point at a point $(x_{0}, y_{0})$ .