Explanation Given Information: The function f ( x , y ) = x 2 + y 2 subject to the constraint 2 x + y = 10 . Formula Used: The extreme value of the function f ( x , y ) subject to the constraint g ( x , y ) can be obtained in the following steps: 1. Form a Lagrange function F ( x , y , λ ) = f ( x , y ) − λ g ( x , y ) . 2. Obtain the solutions for the system F x = 0 , F y = 0 , F λ = 0 as ( x , y , λ ) . 3. Then check whether the solution ( x , y ) is a maximum or a minimum value using test values from the constraints. Calculation: Consider the function, f ( x , y ) = x 2 + y 2 Rewrite the provided constraint as: 2 x + y = 10 2 x + y − 10 = 0 Now, form a new function F given by, F ( x , y , λ ) = x 2 + y 2 − λ ( 2 x + y − 10 ) Find F x , F λ and F y . For F x , x is treated as variable and y and λ are treated as constants and the equation is differentiated. F x = 2 x − 2 λ ….. ( 1 ) For F y , y is treated as variable and x and λ are treated as constants and the equation is differentiated. F y = 2 y − λ ….. ( 2 ) For F λ , λ is treated as variable and x and y are treated as constants and the equation is differentiated

12th Edition

ISBN: 9780135165928

Author: BITTINGER

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 6.5, Problem 4E

To determine

To calculate: The extremum of f(x,y)=x2+y2 subject to the constraint 2x+y=10 and state whether it is a maximum or a minimum.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.5, Problem 3E

Chapter 6.5, Problem 5E

Students have asked these similar questions

Given lim x-4 f (x) = 1,limx-49 (x) = 10, and lim→-4 h (x) = -7 use the limit properties to find lim→-4 1 [2h (x) — h(x) + 7 f(x)] : - h(x)+7f(x) 3 O DNE

17. Suppose we know that the graph below is the graph of a solution to dy/dt = f(t). (a) How much of the slope field can you sketch from this information? [Hint: Note that the differential equation depends only on t.] (b) What can you say about the solu- tion with y(0) = 2? (For example, can you sketch the graph of this so- lution?) y(0) = 1 y AN

(b) Find the (instantaneous) rate of change of y at x = 5. In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the following limit. lim h→0 - f(x + h) − f(x) h The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule defining f. f(x + h) = (x + h)² - 5(x+ h) = 2xh+h2_ x² + 2xh + h² 5✔ - 5 )x - 5h Step 4 - The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x). - f(x + h) f(x) = = (x² x² + 2xh + h² - ])- = 2x + h² - 5h ])x-5h) - (x² - 5x) = ]) (2x + h - 5) Macbook Pro

Chapter 6 Solutions

CALCULUS+ITS APPLICATIONS (LL)

Ch. 6.1 - 2. . Ch. 6.1 - Forf(x,y)=x23xy,find(0,2),f(2,3),andf(10,5).Ch. 6.1 - Prob. 3E Ch. 6.1 - 3. . Ch. 6.1 - 6. . Ch. 6.1 - Forf(x,y)=Inx+y3,findf(e,2),f(e2,4),andf(e3,5).Ch. 6.1 - 8. . Ch. 6.1 - Forf(x,y,z)=x2y2+z2,findf(1,2,3)andf(2,1,3).Ch. 6.1 - In Exercises 9-14, determine the domain of each...Ch. 6.1 - In Exercises 9-14, determine the domain of each...

Additional Math Textbook Solutions

Find more solutions based on key concepts

Stem plots. In Exercises 7 and 8, construct the stemplot. 7. Pulse Rates Refer to the data listed in Exercise 5...

Elementary Statistics (13th Edition)

Assessment 1-1A How many triangles are in the following figure?

A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)

A student has to sell 2 books from a collection of 6 math, 7 science, and 4 economics books. How many choices a...

A First Course in Probability (10th Edition)

Interpreting a Decision In Exercises 43–48, determine whether the claim represents the null hypothesis or the a...

Elementary Statistics: Picturing the World (7th Edition)

1. combination of numbers, variables, and operation symbols is called an algebraic______.

Algebra and Trigonometry (6th Edition)

To write the expression using positive exponent

Pre-Algebra Student Edition

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.

The extremum of f ( x , y ) = x 2 + y 2 subject to the constraint 2 x + y = 10 and state whether it is a maximum or a minimum.

Solution Summary: The author explains how the extremum of f(x,y) is subject to the constraint 2x+y=10.

Videos

To calculate: The extremum of f(x,y)=x2+y2 subject to the constraint 2x+y=10 and state whether it is a maximum or a minimum.

Want to see the full answer?

Chapter 6 Solutions

Additional Math Textbook Solutions