SOLUTION: In Exercises 2-6, find two positive numbers that satisfy the given requirements. The second number is the reciprocal of the first and their sum is minimum.

Question 698471: In Exercises 2-6, find two positive numbers that satisfy the given requirements.
The second number is the reciprocal of the first and their sum is minimum.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
find two positive numbers that satisfy the given requirements.
The second number is the reciprocal of the first and their sum is minimum.
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1st; x
2nd: 1/x
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Equation:
S(x) = x + (1/x)
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S(x) = (x^2+1)/x
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Take the derivative:
S'(x) = [x(2x)- (x^2+1)]/x^2
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Find the zeroes:
[2x^2 - x^2 - 1] / x^2 = 0
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(x^2-1) = 0
x = 1 or x = -1
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Max = 1+(1/1) = 2
Min = -1+ (1/-1) = -1-1 = -2
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Cheers,
Stan H.
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