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determine intervals on which cost is increasing

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If we use the following function to model the cost of production, determine the intervals on which the cost is increasing or decreasing.

C(x) = 5 ( 2/x + x/(x+2))

Identify the critical points for the function.

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C(x) = 5(2/x + x/(x+2)) = 5(2/x + 1 - 2/(x+2))
So we set C'(x) = 5(-2/x^2 + 2/(x+2)^2) = 0
Thus we get 1/x^2 = 1/(x+2)^2, then (x+2)^2 = ...

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