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Find two positive real numbers whose product is a maximum. the sum is 80
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Find two positive real numbers whose product is a maximum. the sum is 80
asked
Nov 6, 2018
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Find two positive real numbers whose product is a maximum. the sum is 80
Mathematics
college
Letfar
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Letfar
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let's say the numbers are "a" and "b"
thus
set the derivative to 0, and check the critical points, there's only one anyway
and do a first-derivative test, to see if it's a maximum
Flotothemoon
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Nov 7, 2018
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Flotothemoon
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xy=max
x+y=80
minus x both sides to solve for y
y=80-x
subsitute
(x)(80-x)=max
80x-x²=max
take the derivitive
80-2x=max'
find where it equalt 0
80-2x=0
80=2x
40=x
at x=40
then y=80-40=40
the numbers are 40 and 40
Keppil
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Nov 11, 2018
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Keppil
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