When is the cost of producing this chemical a minimum?

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The production cost per kilogram, \(C\) (in thousands of pounds) when \(x\) kilograms of a chemical are made is given by \[ C=3x+\frac{100}{x},\; x>0. \] Find the value of \(x\) for which the cost is a minimum, and the minimum cost. Show, also, that this cost is a minimum rather than a maximum.