5. (10%) For the equation y2 — yex — xlny = 12, the slope of the tangent line at the point (1,1) =____

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Chia Chung

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2022/08/13

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9. (10%) A closed rectangular box whose volume is 128 cubic inches is to be made with a square base. If the material for the top and bottom costs twice as much per square inch as the material for the sides, use Lagrange Multipliers to find the dimensions of the box that minimize the cost of material.

5. (10%) For the equation y² — ye^x — xlny = 12, the slope of the tangent line at the point (1,1) =____

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