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anonymous

  • 5 years ago

Minimum surface area box: All boxes with a square base and a volume of 50ft^3 have a surface area given by S(x)=2x^2+200/x, where x is the length of the sides of the base. Find the absoulte minimum of the surface area function. What are the dimensions of the box with minimum surface area?

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  1. anonymous
    • 5 years ago
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    take the derivative of the surface area function. dS/dx = 4x - 200/(x^2) Set it equal to 0 because that is where extrema occur 0 = 4x -200/(x^2) 200 = 4x^3 50 = x^3 x = 3.68

  2. anonymous
    • 5 years ago
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    Thank you so much!

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