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Asked by
Sandhya
Express the number 25 as a sum of two nonnegative numbers whose product is as large as possible.
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Answered by
Anonymous
25=a+b
b=25-a
a*b=a*(25-a)=25a-a^2
First derivative=25-2a
Function has maximum when first derivative=0 and second derivative<0
25-2a=0
25=2a Divide with 2
a=12.5
Second derivative= -2
That is maximum.
b=25-a
b=25-12.5
b=12.5
25=12.5+12.5
Answered by
shay
12.5 and 12.5
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