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Question

e calculus que ×0e6(14PTs Co s ie Search Textb X Chegg Study ×? 6 14PTs Corxye Math 23 Te X ? Math 123 Se x .29bS 0219 ?? 58 HowDe X ? secure ! https://d21.sdbor.edu/d2l/le/content/1029151/viewContent/5994809/View 9- (7 PTS) A company wishes to manufacture a box with a square base, an open top, and a volume of 32 cm Find the dimensions of the box that minimizes the amount of material used using methods of calculus shown in class. Find the dimensions of the box that minimizes the amount of material used b. Verify that your answer is a minimum a. 2:47 ovUS

Explanation / Answer

Volume = x2y

32 = x2y

y = 32 /x2

S = x2+ 4 xy

S = x2+ (128/x)

S' = 2x - (128/x2)

S ' =0

2x-(128/x2) =0

x3=64

x = 4

y=32/x2 = 32/ 16 = 2

So the dimension of the box is x=4 cm and y = 2 cm.

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