Math, asked by shuheb5783, 10 months ago

Find max value of xy subject to x+y=8

Answers

Answered by zahaansajid
2

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For the value of xy to be maximum,

\frac{d(xy)}{dx} = 0 \\

Since xy has 2 variables we cannot differentiate it

It is given that,

x + y = 8

y = 8 - x

Substituting this in the equation,

\frac{d(xy)}{dx} = \frac{d[x(8 - x)]}{dx} =\frac{d(8x - x^{2}) }{dx} = 0

8 - 2x = 0\\2x = 8\\x = 4

Therefore,

x = 4

y = 8 - x = 8 - 4 = 4

Therefore the maximum value of xy = 4*4 = 16

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Answered by srisakethsimha
0

Answer:

16

Step-by-step explanation:

  1. if x=8 then y=0

or

y=8 then x=0

then xy=0

2. if x=7 then y=1

or

x=1 then y=7

then xy=7

3. if x=6 then y=2

or

x=2 then y=6

then xy =12

4. if x=5 then y=3

or

x=3 then y=5

then xy =15

5. if x=4 then y=4

then xy=16

therefore xy=16

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