Math

Express the number 25 as a sum of two nonnegative numbers whose product is as large as possible.

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  1. 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

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  2. 12.5 and 12.5

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