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

Answer 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

Answer 2

12.5 and 12.5