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Calculus Optimization Problem 1 Minimize the Surface Area of a Cylinder

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This presentation demonstrates, given a cylinder (can) of a certain volume, how to find the height of the can that minimizes the surface area required to construct a can of that volume. The problem involves using a volume formula to express the radius of the can as a function of its height, plugging that value of r into the surface area formula for a cylinder, finding the first derivative of the surface area function, setting the value of the derivative equal to zero, then solving for the unknown, height.

posted by danielcc19zm