SOLUTION: Help find two numbers whose sum is 700 and whose product is a maximum.

Question 873702: Help find two numbers whose sum is 700 and whose product is a maximum.
Found 2 solutions by KMST, Fombitz:
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
= one of the numbers.
= the other number.
= the product of those two numbers.
That is a quadratic function, and is usually written as
.
The graph is a parabola, looking like this: .
Where is its maximum?
You may have been shown, and it can be proven that the maximum of a quadratic like
is at
So in this case the maximum happens when
.
Of course, that means that the other number is
.
That is not surprising because it is the same as asking you what rectangle with a half-perimeter of 700 has the greatest area, and we know it is a square.
The same problem could also be asked as what is the largest rectangular plot that can be fenced when you have 1400 feet of fencing.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

Find df/dA.

Set it equal to zero to find the maximum.

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