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$y = \sqrt((x -16)^2 + (x - 6)^2) + \sqrt((x - q)^2 + (x- (-q +10))^2) + \sqrt((q + 7)^2 + ((-q+10) -13)^2)$

where ${x >= 10}$

${x<=20}$

${q>=-10}$

${q <= 0}$

${-q + 10 >= 10}$

${-q +10 <= 20}$

I know how to minimise a function with 1 variable. I know derivatives/intergrals

For more information the function is the distance between two points passing through two lines. In future I would like to add more lines.

Jean-Claude Lemieux
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    You would take what are called partial derivatives of the function with respect to $x$ and $q$. Then you'd set both of these equal to zero in the same way as in 1D. After that, you should solve to find the $(x,q)$ which make it equal zero.

    This is your minima, unless it is just a local minimum. Also check the end points to see if they are lower.

     – fGDu94 Jul 15 '19 at 23:34
  • If I add more lines it wont work ? – Jean-Claude Lemieux Jul 16 '19 at 00:32
  • Welcome to the site ! Would you mind to fix the edit of the expression since it is quite difficult to read ? Have a look at https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference . Thanks. By the way, where are you located (I am in Pau) ? – Claude Leibovici Jul 16 '19 at 04:28

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