Question

The sum of two nonnegative numbers is 50. What is the maximum value of the product of these two numbers ?

Answer 1

625

Explanation:

Let two number be x and (50-x).

The product of numbers be x(50-x).

P = 50x-x²

For maximizing the product,

`(dP)/(dx)=0\\\\(d)/(dx)(50x-x^2)=0\\\\50-2x=0\\\\50=2x\\\\x=25`

So, the maximum product, P = 50(25)-(25)²

P = 625

Hence, the maximum value of the product of these two numbers is 625.