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    Find the maximal and minimal by derivatives

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    Please help me with the following calculus problem:

    1. A homeowner wants to enclose a 5,800 square feet rectangular garden by a fence in his backyard. If three sides of the fence cost $6.25 per foot and 4th side costs $10.25 per foot, find the dimensions that will minimize the cost of building the fence and the minimum cost of its construction.

    2. Find the absolute extreme values of f(x) = x^4 + 8x^3 - 32x^2 on interval [-1, 5].

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    Solution Preview

    1. Suppose the length is x feet, width is y feet.
    we could have xy=5800.
    cost z=6.25*(2x+y)+10.25y

    z=12.5*5800/y+16.5y=72500/y+16.5y
    z'=-72500/y^2+16.5.
    when z'=0, y=66.29 ...

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    The solution provides detailed explanation how to find the maximal and minimal by derivatives.

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