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.