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Graphical meaning of tangent in optimization problem

  1. Jun 9, 2015 #1
    In a trivial optimization problem, when seeking the value of x2 that minimizes y(x2)/(x2-x1), the solution is graphically given by the tangent line shown in the figure.

    I'm having a lot of difficulty understanding why this is true, i.e., the logical steps behind the equivalence supporting the solution, either via calculus, algebraic, or geometric reasoning.
  2. jcsd
  3. Jun 9, 2015 #2


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    Are you sure that you have given all information? The curve looks suspiciously like y = x2.
  4. Jun 9, 2015 #3
    @Svein: Sorry, x1 and x2 mean x_1 and x_2.
  5. Jun 10, 2015 #4


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    If we have no information on y(x) or on x1, it is impossible to answer. If we assume y = x2, it is at least possible: Minimize x2/(x-x1). Assuming that it exists, use the rule for deriving a fraction and see if it can be equal to 0.
  6. Jun 10, 2015 #5
    I think you need this
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