Question 1120635: Find two numbers whose product is 120 and whose sum is a minimum.
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443)   (Show Source):
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
Minimize
\ =\ x\ +\ \frac{120}{x})
\ =\ 1\ -\ \frac{120}{x^2})
Set the derivative equal to zero and solve.
If you choose the negative root, then there is no minimum, because, for all negative values of the independent variable, the 2nd derivative is negative,  , proving that the negative value is a local maximum. But since the 2nd derivative is positive for all positive values of the independent variable, the positive root provides a local minimum. Note that the question very cleverly asks for "a" minimum, not "the" minimum.
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John
My calculator said it, I believe it, that settles it
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