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Math Help - optimization - distance on a pipeline

  1. #1
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    optimization - distance on a pipeline

    A pipeline is to be placed so that it connects point A to the river point B. A and B are two homesteads and X is the pumphouse. How far from M should X be so that the pipeline is as short as possible?
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  2. #2
    Eater of Worlds
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    Use a little Pythagoras on the two right triangles.

    Let L=length of pipeline. Let x=length from M to X.

    L=\sqrt{1+(5-x)^{2}}+\sqrt{x^{2}+4}

    Differentiate, set to 0 and solve for x
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