Explanation Given: The given function is, f ( x , y ) = x y + y − 2 x . Approach: “For a function z = f ( x , y ) , let f x x , f y y , and f x y all exist in a circular region contained in the xy -plane with center ( a , b ) . Further, let f x ( a . b ) = 0 and f y ( a . b ) = 0 . Define the number D , known as the discriminant by, D = f x x ( a , b ) ⋅ f y y ( a , b ) − [ f x y ( a , b ) ] 2 Then, a. f ( a , b ) is a relative maximum if D > 0 and f x x ( a , b ) < 0 . b. f ( a , b ) is a relative minimum if D > 0 and f x x ( a , b ) > 0 . c. f ( a , b ) is a saddle point (neither a maximum nor a minimum) if D < 0 . d. if D = 0 , the test gives no information.” Calculation: Consider the given function, f ( x , y ) = x y + y − 2 x . Obtain f x ( x , y ) , and f y ( x , y ) as follows. f x ( x , y ) = ∂ ∂ x ( x y + y − 2 x ) = y − 2 and, f y ( x , y ) = ∂ ∂ y ( x y + y − 2 x ) = x + 1 The function has relative extrema at a point, if

2nd Edition

ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

See similar textbooks

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Videos

Question

Chapter 9.3, Problem 1E

To determine

To find:

All the points for relative extrema or identify any saddle point for the function f(x,y)=xy+y−2x.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.3, Problem 2YT

Chapter 9.3, Problem 2E

Students have asked these similar questions

Solve : X + sin x = 0. By the false positioning numerical method

Solve: X + sin X = 0 by the false positionining numerical method

On from the equation: 2 u = C₁ + C₂ Y + Czy + Cu y³ Find C₁, C₂, C3 and Cy Using these following Cases : (a) 4=0 at y=0 (b) U = U∞ at y = 8 du (c) at Y = S ду --y. ди = 0 at y = 0 буг

Chapter 9 Solutions

Calculus For The Life Sciences

Ch. 9.1 - YOUR TURN For the function in Example 1, find...Ch. 9.1 - Prob. 2YT Ch. 9.1 - Prob. 3YT Ch. 9.1 - EXERCISES Let f(x,y)=2x3y+5.Find the following. a....Ch. 9.1 - Prob. 2E Ch. 9.1 - EXERCISES Let h(x,y)=x2+2y2. Find the following....Ch. 9.1 - EXERCISES Let f(x,y)=9x+5ylogx. Find the...Ch. 9.1 - EXERCISES Let f(x,y)=ex+ln(x+y). Find the...Ch. 9.1 - EXERCISES Let f(x,y)=xex+y. Find the following. a....Ch. 9.1 - EXERCISES Let f(x,y)=xsin(x2y). Find the...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

All the points for relative extrema or identify any saddle point for the function f ( x , y ) = x y + y − 2 x .

Solution Summary: The author explains that the given function is f(x,y)=xy+y-2x.

Concept explainers

Videos

To find:

All the points for relative extrema or identify any saddle point for the function f(x,y)=xy+y−2x.

Want to see the full answer?

Chapter 9 Solutions

All the points for relative extrema or identify any saddle point for the function f ( x , y ) = x y + y − 2 x .

Solution Summary: The author explains that the given function is f(x,y)=xy+y-2x.

Concept explainers

Videos

To find: All the points for relative extrema or identify any saddle point for the function f(x,y)=xy+y−2x.

Want to see the full answer?

Chapter 9 Solutions

To find:

All the points for relative extrema or identify any saddle point for the function f(x,y)=xy+y−2x.