SOLUTION: THE SUM OF TWO POSTIVE WHOLE NUMBERS IS 96. WHAT IS THE GREATEST POSSIBLE PRODUCT OF TWO POSITIVE WHOLE NUMBERS WHOSE SUM IS 96?
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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): You can put this solution on YOUR website!
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Let 
represent one of the numbers. Then the other number is 
Then we want to maximize \ =\ 96x\ -\ x^2)
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.
\ =\ 96\ -\ 2x)
\ =\ -2\ <\ 0\ \forall x\ \in\ \mathbb{R})
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 
}\ =\ 48)
Same answer.
John
My calculator said it, I believe it, that settles it
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