Explanation Given Information: The function f ( x , y ) = x y subject to the constraint x − y = 4 . 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 y Rewrite the provided constraint as: x − y = 4 x − y − 4 = 0 Now, form a new function F given by, F ( x , y , λ ) = x y − λ ( x − y − 4 ) Find F x , F λ and F y . For F x , x is treated as variable z , y and λ are treated as constants and the equation is differentiated. F x = y − λ ….. ( 1 ) For F y , y is treated as variable and x , z and λ are treated as constants and the equation is differentiated. F y = x + λ ….. ( 2 ) For F , λ is treated as variable and x and y are treated as constants and the equation is differentiated

12th Edition

ISBN: 9780136423287

Author: BITTINGER

Publisher: PEARSON

See similar textbooks

Question

Chapter 6.5, Problem 15E

To determine

To calculate: The two numbers that have minimum product among numbers with difference 4.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.5, Problem 14E

Chapter 6.5, Problem 16E

Students have asked these similar questions

4. AP CalagaBourd Ten the g stem for 00 3B Quiz 3. The point P has polar coordinates (10, 5). Which of the following is the location of point P in rectangular coordinates? (A) (-5√3,5) (B) (-5,5√3) (C) (5√3,5) (D) (5√3,-5) 7A 6 2 3 4 S 元 3 داند 4/6 Polar axis -0 11 2 3 4 4 5л 3 Зл 2 11π 6 rectangular coordinates of K? The figure shows the polar coordinate system with point P labeled. Point P is rotated an angle of measure clockwise about the origin. The image of this transformation is at the location K (not shown). What are the (A) (-2,2√3) (B) (-2√3,2) (C) (2,-2√3) D) (2√3,-2) T 2

AP CollegeBoard 3B Quiz 1. 2. y AP PRECALCULUS Name: od to dove (or) slog mig Test Boc 2л The figure gives the graphs of four functions labeled A, B, C, and D -1 in the xy-plane. Which is the graph of f(x) = 2 cos¹x ? m -3 π y 2- 1 3 (A) A (B) B 2 A B C D D -1- -2- Graph of f -2 -1 3. 2- y' Graph of g 1 2 1 3 y = R 2/01 y = 1 + 1/2 2 3 4 5 y= = 1-777 2 (C) C (D) D Which of the following defines g(x)? The figure gives the graphs of the functions ƒ and g in the xy-plane. The function f is given by f(x) = tan-1 EVES) (A) (A) tan¹x+1 (B) tan¹ x + 1/ (C) tan¹ (2) +1 (D) tan¹() + (B) Vs) a I.

Consider the region below f(x) = (11-x), above the x-axis, and between x = 0 and x = 11. Let x; be the midpoint of the ith subinterval. Complete parts a. and b. below. a. Approximate the area of the region using eleven rectangles. Use the midpoints of each subinterval for the heights of the rectangles. The area is approximately square units. (Type an integer or decimal.)