SOLUTION: find two numbers whos sum is 21 and whose product is a maximum

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Question 822167: find two numbers whos sum is 21 and whose product is a maximum
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Let us assume one of the numbers is x. As the sum of the two numbers is 21, the other number is 21-x.
The product of the two numbers is a function f%28x%29+=+x%2A%2821-x%29+=+21x-+x%5E2.
Now we need to find the maximum +value of f%28x%29.
For this we need the derivative of f%28x%29 and have to equate it to 0.
f’%28x%29+=+21+%96+2x+=+0
=> 10.5+%96+x+=0
=> x+=10.5
Now f’’%28x%29+=+-2 which is negative at x=10.5. So f+%2810.5%29 is truly the maximum+value.
If x=10.5, the first number is 10.5 and the second number is 21-10.5+=+10.5
So the two required numbers are 10.5 and 10.5
+graph%28+600%2C+600%2C+-15%2C+35%2C+-10%2C+115%2C+-x%5E2%2B21x%29+