(a) Looking at your picture, identify the minimum and maximum of f subject to the given constranit. (b) Use the method of Lagrange multipliers to confirm your geometric reasoning. 8. Sketch the level curves f(x, y) = c of f(x, y) = 2x – y for c = 8. -3,-2,-1,0, 1, 2, and 3. In the same coordinate system, sketch the graph of the constraint x2 + y² = 1. (a) Looking at your picture, identify the minimum and maximum of f subject to the given constraint. (b) Use the method of Lagrange multipliers to obtain the desired constrained minimum and maximum algebraically. 9. State the problem in Example 4.26 in Section 4.3 as a constrained optimization problem and solve it using Lagrange multipliers. 10. Explain why it does not make much sense to develop the Lagrange multipliers method to optimize a function f(x, y) of two variables subject to two constraints g1(x, y) = kj and g2(x, y) = k2- Exercises 11 to 19: Find the extreme values (if any) of a function f subject to the given constraint. 11. f(x, y) = 3xy; x² + y² = 4 12. f(x, y)= 4-x2 - y²; y – 2x = 1 (Hint: Find the maximum; argue that a minimum does not %3D exist.) 13. f(x, y) = 2x² – y²; x² + y? = 1 %3D flxiy)=-3 f(ag)=D-2 frsiy)=2 f(h.y) = 3 -3

(a) Looking at your picture, identify the minimum and maximum of f subject to the given constranit. (b) Use the method of Lagrange multipliers to confirm your geometric reasoning. 8. Sketch the level curves f(x, y) = c of f(x, y) = 2x – y for c = 8. -3,-2,-1,0, 1, 2, and 3. In the same coordinate system, sketch the graph of the constraint x2 + y² = 1. (a) Looking at your picture, identify the minimum and maximum of f subject to the given constraint. (b) Use the method of Lagrange multipliers to obtain the desired constrained minimum and maximum algebraically. 9. State the problem in Example 4.26 in Section 4.3 as a constrained optimization problem and solve it using Lagrange multipliers. 10. Explain why it does not make much sense to develop the Lagrange multipliers method to optimize a function f(x, y) of two variables subject to two constraints g1(x, y) = kj and g2(x, y) = k2- Exercises 11 to 19: Find the extreme values (if any) of a function f subject to the given constraint. 11. f(x, y) = 3xy; x² + y² = 4 12. f(x, y)= 4-x2 - y²; y – 2x = 1 (Hint: Find the maximum; argue that a minimum does not %3D exist.) 13. f(x, y) = 2x² – y²; x² + y? = 1 %3D flxiy)=-3 f(ag)=D-2 frsiy)=2 f(h.y) = 3 -3

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 12T

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