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More Calculus

Applications of the Derivative

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Related Rates

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The First Derivative and the Behavior of Functions

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The Second Derivative and the Behavior of Functions

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Optimization

A rectangular box with an open top is to be made from a \(10\)-in.-by-\(16\)-in. piece of cardboard by removing small squares of equal size from the corners and folding up the remaining flaps. What should be the size of the squares cut from the corners so that the box will have the largest possible volume?

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Applications in Business and Economics

A company estimates that the weekly sales \(q\) of its product is related to the productâ€™s price \(p\) by the function \[q=\frac{4\text{,}500}{\sqrt[3]{p^2}}\] where \(p\) is in dollars. Currently, each unit of the product is selling for \(\$27\). Determine the point elasticity of demand of this product.