mathman3208 mathman3208
  • 18-09-2017
  • Mathematics
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The pair of numbers whose sum is 8 and whose product is as large as possible is

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apologiabiology
apologiabiology apologiabiology
  • 18-09-2017
x and y are the numbers

x+y=8

and product is max
xy=max
ok

x+y=8
minus x both sides
y=8-x
subsitute 8-x for y in other equation

(8-x)(x)=max
8x-x²=max
take derivitive
8-2x=dy/dx max
find where it equal 0
8-2x=0
8=2x
4=x

at x=4

y=8-x
y=8-4
y=4


the numbers are 4 and 4

their product is 4*4 or 16
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