Question

What is the maximum possible product of two numbers that have a sum of 56?

A) 28
B) 784
C) 1400
D) 56

Answer 1

To find the maximum possible product of two numbers that have a sum of 56, we can use the concept of maximizing the product of two numbers when their sum is given. The maximum possible product is 784.

Step-by-step explanation:

To find the maximum possible product of two numbers that have a sum of 56, we can use the concept of maximizing the product of two numbers when their sum is given.

1. Let's assume the first number is x. The second number can be represented as 56 - x, since their sum is 56.
2. The product of the two numbers is x(56 - x), which can be simplified to 56x - x^2.
3. To find the maximum possible product, we can take the derivative of the product function and set it equal to zero.
4. The critical points of the derivative are at x = 28 and x = 0. However, x = 0 is not a valid solution because we need positive numbers.
5. So, the maximum possible product occurs when x = 28. Plugging this value into the product function, we get 784.

Therefore, the maximum possible product of two numbers that have a sum of 56 is 784.