SOLUTION: The second number is the reciprocal of the first number and the sum is the minimum.

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Question 988985: The second number is the reciprocal of the first number and the sum is the minimum.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= the first number, so
1%2Fx= the second number = the reciprocal of the first number, and
S=x%2B1%2Fx= the sum.
The derivative is
dS%2Fdx=1-1%2Fx%5E2=%28x%5E2-1%29%2Fx%5E2=%28x%2B1%29%28x-1%29%2Fx%5E2
dS%2Fdx is positive for x%3C-1, meaning that S is increasing in %22%28%22-infinity%22%2C%22-1%22%29%22 .
dS%2Fdx is negative for -1%3Cx%3C1, meaning that S is decreasing in %22%28%22-1%22%2C%221%22%29%22 .
dS%2Fdx=0 for x=-1, where S has a maximum.
dS%2Fdx is positive for x%3E1, meaning that S is increasing in %22%28%221%22%2C%22infinity%22%29%22 .
dS%2Fdx=0 for highlight%28x=1%29, where S has a minimum.