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webassign.netTexas A&MUconnect L..https://tam...CengageCengageCengageraight28. 0/1 points| Previous Answers OSCalc1 14.8.369.Minimize f(x, y) x +y on the hyperbola xy = 5.angaXrom RadiotAdditional MaterialsopaleBooksymphoniesover WeeklySubmit AnswerSave ProgressPractice Another Versionpel29.-1 points OSCalc1 14.8.371.ckMaximize f(x, y, z) = 2x + 7y +9z on the sphere x+ y + z - 67.anoldplay+) New PlaylistChristus anAdditional MaterialsLudwigvarGUNMIWPXO8 a20MacBook ProSCFIF3F4F5F6F8F9OtO#$%&246WwQERTYADFKZXCBOtAA3

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Uconnect L..
https://tam...
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raight
28. 0/1 points| Previous Answers OSCalc1 14.8.369.
Minimize f(x, y) x +y on the hyperbola xy = 5.
anga
X
rom Radio
t
Additional Materials
op
al
eBook
symphonies
over Weekly
Submit Answer
Save Progress
Practice Another Version
pel
29.
-1 points OSCalc1 14.8.371.
ck
Maximize f(x, y, z) = 2x + 7y +9z on the sphere x+ y + z - 67.
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F6
F8
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webassign.net Texas A&M Uconnect L.. https://tam... Cengage Cengage Cengage raight 28. 0/1 points| Previous Answers OSCalc1 14.8.369. Minimize f(x, y) x +y on the hyperbola xy = 5. anga X rom Radio t Additional Materials op al eBook symphonies over Weekly Submit Answer Save Progress Practice Another Version pel 29. -1 points OSCalc1 14.8.371. ck Maximize f(x, y, z) = 2x + 7y +9z on the sphere x+ y + z - 67. ano ldplay +) New Playlist Christus an Additional Materials Ludwig var GUNMI WPXO8 a 20 MacBook Pro SC FI F3 F4 F5 F6 F8 F9 OtO # $ % & 2 4 6 Ww Q E R T Y A D F K Z X C B O tAA 3

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Step 1

The given function of hyperbola can be written in terms of y as:

 

Plugging this value in the objective function:

ツ=5
5
y =-
f x y
+
2
5
fx
x
52
f x
2
25
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ツ=5 5 y =- f x y + 2 5 fx x 52 f x 2 25

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Step 2

A function has a minimum or maximum value when the first derivative of the function is 0.

Applying derivative with respect to x.

 

Setting the first derivative to 0 to solve for x:

25
f x
х"
f = x +25x2
)
f(2x)25-2x
f'3 2х -50х-3
f'= 0
2х - 50х
0
25
х
..3
х*
25
10
x
3
х
x* -25
0
4
x25 0
4
х*
25
help_outline

Image Transcriptionclose

25 f x х" f = x +25x2 ) f(2x)25-2x f'3 2х -50х-3 f'= 0 2х - 50х 0 25 х ..3 х* 25 10 x 3 х x* -25 0 4 x25 0 4 х* 25

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Step 3

Plugging the value of x to obtain the value of y,

When

 

When

 

Here for both the values of x...

5
= 5
y =
V5
5
-V5
xニー5 y=ー5
x25, y5
f x y
f 5+5
f 10
help_outline

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5 = 5 y = V5 5 -V5 xニー5 y=ー5 x25, y5 f x y f 5+5 f 10

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Tagged in

Math

Calculus

Derivative

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