SOLUTION: Not sure which topic would fit this best... but if someone could show me how to tackle this question: The sum of two numbers is 30 and their product is a maximum. Find the two n

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Question 214564: Not sure which topic would fit this best... but if someone could show me how to tackle this question:
The sum of two numbers is 30 and their product is a maximum. Find the two numbers.
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
Not sure which topic would fit this best... but if someone could show me how to tackle this question:
The sum of two numbers is 30 and their product is a maximum. Find the two numbers.
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It's always the square, in this case 15 and 15.
15*15 = 225
14*16 = 224
13*17 = 221
See the pattern?
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A rigorous solution:
x*(30-x) = 0
x^2 - 30x = 0
The vertex (maximum) is at x = -b/2a
= 30/2 = 15
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Using calculus:
f(x) = x*(30-x)
f(x) = x^2 - 30x
f'(x) = 2x-30 = 0
2x-30 = 0
x = 15