Find all the local maxima, local minima, and saddle points of the functions in Exercises 1–3. ' 1. ƒ(x, y) = 5xy - 7x2 + 3x - 6y + 2 2. ƒ(x, y) = 2xy - x2 - 2y2 + 3x + 4 3. ƒ(x, y) = x2 - 4xy + y2 + 6y + 2

Find all the local maxima, local minima, and saddle points of the functions in Exercises 1–3. ' 1. ƒ(x, y) = 5xy - 7x2 + 3x - 6y + 2 2. ƒ(x, y) = 2xy - x2 - 2y2 + 3x + 4 3. ƒ(x, y) = x2 - 4xy + y2 + 6y + 2

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.3: Algebraic Expressions

Problem 20E

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Concept explainers

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

Question

Find all the local maxima, local minima, and saddle points of the functions in Exercises 1–3. '

1. ƒ(x, y) = 5xy - 7x2 + 3x - 6y + 2

2. ƒ(x, y) = 2xy - x2 - 2y2 + 3x + 4

3. ƒ(x, y) = x2 - 4xy + y2 + 6y + 2

Formula Formula A function f ( x ) is also said to have attained a local minimum at x = a , if there exists a neighborhood ( a − δ , a + δ ) of a such that, f ( x ) > f ( a ) , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a f ( x ) − f ( a ) > 0 , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a In such a case f ( a ) is called the local minimum value of f ( x ) at x = a .

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