8. Find the maximum and minimum values of f(x,y) = x³y* subject to the constraint 5x2+ 2y2 = 14. 5x +2y? - 14 =6 33

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.3: Rates Of Change
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8. Find the maximum and minimum values of f (x, y) = x³y* subject to the
constraint 5x2 + 2y2 = 14.
5x +2y?-14 =6
vg= < 10%, Ay)
4.
3x
= 1oxx
Ay A
49
5x+ 2y- 14 =0
5x²+ 2 (3.3x*)- 14=0
5x+ b.bx² - 14 =6
1.しx? = 14
%3D
3 2
= 10 x (X y
3
3x²
y= 3.3x9
3x
2
11.6
2.
X = 1.09858
y = 3.3x
y= 3.3 (1.2)
y?= 3.16
f(1.099, 1.989). (11) (1.499)*
20.774L
f (1o99, -1.99) =
f(-1099, 1989) =
f(-1049, - 1.09)
26.7746 MAX
y =#1, 989
Nin gott2 -
= - 20-774
Transcribed Image Text:8. Find the maximum and minimum values of f (x, y) = x³y* subject to the constraint 5x2 + 2y2 = 14. 5x +2y?-14 =6 vg= < 10%, Ay) 4. 3x = 1oxx Ay A 49 5x+ 2y- 14 =0 5x²+ 2 (3.3x*)- 14=0 5x+ b.bx² - 14 =6 1.しx? = 14 %3D 3 2 = 10 x (X y 3 3x² y= 3.3x9 3x 2 11.6 2. X = 1.09858 y = 3.3x y= 3.3 (1.2) y?= 3.16 f(1.099, 1.989). (11) (1.499)* 20.774L f (1o99, -1.99) = f(-1099, 1989) = f(-1049, - 1.09) 26.7746 MAX y =#1, 989 Nin gott2 - = - 20-774
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