Question

the sum of two numbers is 50.what is the smallest possible product of the two numbers?

Answer 1

1 * 49?

Answer 2

use of derivatives

Answer 3

first number ---- x

second number ---- 50-x
Product ---- p

p = x(50-x) = 50x - x^2

this is represented by a downwards parabola which would have a
maximum, not a minimum
Check the wording of the question.

e.g.
dp/dx = 50 - 2x = 0 for a maximum of p
2x = 50
x = 25
When the two numbers are 25 each, their product will have a maximum of 625
e.g. if one number is 1, the other is 49, and their product is 49, as Ms. Sue had
if one number is .001, the other is 49.999 and their product is .049999 which is less than 49
if one number is -10, the other is 60 , and their product is -600 which is less than the above

As you can see, there is no minimum value.

Answer 4

[AI-generated answer — Explain Bot]

To find the smallest possible product of the two numbers, we need to determine the numbers that can result in the smallest product when their sum is 50.

Let's assume the two numbers are x and y. According to the given information, the sum of the two numbers is 50:

x + y = 50

To find the smallest possible product, we need to consider the scenario where one number is as small as possible and the other number is as large as possible.

In this case, let's assume one number is 1 and the other number is (50 - 1) = 49:

x = 1
y = 49

The product of these two numbers is:

Product = x * y = 1 * 49 = 49

Therefore, the smallest possible product of the two numbers whose sum is 50 is 49.