Question 337695: THE SUM OF TWO POSTIVE WHOLE NUMBERS IS 96. WHAT IS THE GREATEST POSSIBLE PRODUCT OF TWO POSITIVE WHOLE NUMBERS WHOSE SUM IS 96? Answer by solver91311(24713) (Show Source):
Typing in all caps is the electronic equivalent of shouting. It is therefore both rude and annoying. Inside voice boys and girls, please.
Let represent one of the numbers. Then the other number is
Then we want to maximize where
Calculus solution:
Set the first derivative of the function equal to zero and solve for the -coordinate of the extreme point. Evaluate the second derivative at the calculated value of to verify that the extreme is a maximum.
Therefore, the function has a maximum at
Algebra solution:
Note that is a quadratic polynomial in with a negative lead coefficient. That means the graph is a parabola opening downward -- and the vertex is the maximum of the function.
, , and
Same answer.
John
My calculator said it, I believe it, that settles it
