The average cost for a company to produce x units of a product is given by the function A(x) = (15x + 200) / x. Use A'(x) to estimate the change in average cost as production goes from 100 units to 101 units. The change in average cost is approximately [ ] dollars.
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Step 1: Find the derivative of the average cost function A(x) with respect to x. Show more…
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The average cost for a company to produce x units of a product is given by the function A(x) = (16x + 1200) / x. Use A'(x) to estimate the change in average cost as production goes from 200 units to 201 units. The change in average cost is approximately dollars.
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The average cost for a company to produce x units of a product is given by the function A(x) = 19x + 450/x. Use A'(x) to estimate the change in average cost as production goes from 150 units to 151 units.
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$\begin{array}{l}{\text { Average cost A manufacturer has determined that the }} \\ {\text { total cost } C \text { of operating a factory is }} \\ {C=0.5 x^{2}+15 x+5000} \\ {\text { where } x \text { is the number of units produced. At what level of }} \\ {\text { production will the average cost per unit be minimized? (The }} \\ {\text { average cost per unit is } C / x .}\end{array}$
Applications of Differentiation
Concavity and the Second Derivative Test
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