3-14 Each of these extreme value problems has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. 3. f(x, y) = x² - y²; x² + y² = 1 4. f(x, y) = 3x + y; x² + y² = 10 5. f(x, y) = xy; 4x² + y² = 8 6. f(x, y) = xe”; r+y2 = 2 7. f(x, y, z) = 2x + 2y + z; x² + y² + z² = 9 8. f(x, y, z) = exy²; 2x² + y² + z² = 24 9. f(x, y, z) = xy²z; x² + y² + z² = 4 10. f(x, y, z) = ln(x² + 1) + In(y² + 1) + ln(z² + 1); x² + y² + z² = 12 21 th =
3-14 Each of these extreme value problems has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. 3. f(x, y) = x² - y²; x² + y² = 1 4. f(x, y) = 3x + y; x² + y² = 10 5. f(x, y) = xy; 4x² + y² = 8 6. f(x, y) = xe”; r+y2 = 2 7. f(x, y, z) = 2x + 2y + z; x² + y² + z² = 9 8. f(x, y, z) = exy²; 2x² + y² + z² = 24 9. f(x, y, z) = xy²z; x² + y² + z² = 4 10. f(x, y, z) = ln(x² + 1) + In(y² + 1) + ln(z² + 1); x² + y² + z² = 12 21 th =
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.6: Quadratic Functions
Problem 36E
Related questions
Question
7
Transcribed Image Text:0
g(x, y) = 8
70
60
50
40
30
20
10
2. (a) Use a graphing calculator or computer to graph the
curves of the form x² + y
circle x² + y² = 1. On the same screen, graph several
just touch the circle. What is the significance of the
= c until you find two that
values of c for these two curves?
(b) Use Lagrange multipliers to find the extreme values of
f(x, y) = x² + y subject to the constraint x² + y² = 1.
Compare your answers with those in part (a).
14. f(x₁,x₂,..., *In)
3-14 Each of these extreme value problems has a solution with
both a maximum value and a minimum value. Use Lagrange
multipliers to find the extreme values of the function subject to
the given constraint.
3. f(x, y) = x² - y²; x² + y² = 1
4. f(x, y) = 3x + y;
x² + y² = 10
5. f(x, y) = xy; 4x² + y² = 8
6. f(x,y) = xe”; x + y = 2
7. f(x, y, z) = 2x + 2y + z; x² + y² + z² = 9
8. f(x, y, z) = exy²;
2x² + y² + z² = 24
9. f(x, y, z) = xy²z;
x² + y² + z² = 4
10. f(x, y, z) = ln(x² + 1) + ln(y² + 1) + In(z² + 1);
x² + y² + z² = 12
+
x² + x² + ... +
15. The method of L
extreme values
Show that the F
f(x, y) = x² +
solved using L
maximum val
16. Find the min
subject to th
has no maxi
17-20 Find the
17. f(x, y, z)=
18. f(x, y, z)
19. f(x, y, z
20. f(x, y, z
21-23 Fin
the inequa
21. f(x,
22. f(x,
23. f(x
24. Co
f
(F
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