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Math Help - Max-min problem; from Strang textbook

  1. #1
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    Max-min problem; from Strang textbook

    Hi today! Just reviewing another max-min problem here (this one is from Calculus by Gilbert Strang).

    Submarines are located at the points (2,0) and (1,1). Choose the slope m that the line y = mx goes between the two submarines but stays as far as possible from the nearest one.

    I found the solution to be 1/3. But, I did not need to use calculus. I found the solution by finding the midpoint of the segment that joins the two submarines (3/2,1/2) and then finding the slope of the line through that point and the origin.

    How do I use calculus to solve this problem? Is my solution considered "correct"? Thanks for any reply!
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  2. #2
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    Re: Max-min problem; from Strang textbook

    Hey zachd77.

    A maximum involves having a zero derivative with a negative second derivative.

    Can you reformulate the problem to get distance as a function so you can find the above quantities?
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  3. #3
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    Re: Max-min problem; from Strang textbook

    The distance from (2,0) to the line is the same as the distance from (1,1) to the line. So you should be able to solve it using trigonometry.

    - Hollywood
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