If the sum of two real number is 21, what is the greatest possible value of their product

Step-by-step explanation:

let th numbers be x and y.

x+y=21

y=21-x

Product P=xy=x (21-x) = 21 x-x^2

P'=21-2x

P'=0 gives 21-2x=0, x=21/2

P"=-2

which is less than 0 at x=21/2

so P is greatest at x=21/2

y=21-21/2=21/2

P=21/2 * 21/2=441/4=110.25