Graphical meaning of tangent in optimization problem

  • #1
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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.
oft.png
 

Answers and Replies

  • #2
Svein
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Are you sure that you have given all information? The curve looks suspiciously like y = x2.
 
  • #3
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@Svein: Sorry, x1 and x2 mean x_1 and x_2.
 
  • #4
Svein
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seeking the value of x2 that minimizes y(x2)/(x2-x1)
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.
 
  • #5
I think you need this
 

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