Find global minimum of the following











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The global minimum value of
$$|cot x – 1| + |cot x – 2| + |cot x – 31| + |cot x – 32| + |cot x – 24| + |cot x – 5| + |cot x – 6|
+ |cot x – 17| + |cot x – 8| + |cot x – 9| + |cot x – 10| + |cot x – 11| + |cot x – 12| $$
Then find $x=operatorname{arcsec}(alpha/beta )$ where it is occurring.






calculus







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  • Done now what ?
    – D.Manek
    Nov 19 at 11:28















up vote
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down vote

favorite












The global minimum value of
$$|cot x – 1| + |cot x – 2| + |cot x – 31| + |cot x – 32| + |cot x – 24| + |cot x – 5| + |cot x – 6|
+ |cot x – 17| + |cot x – 8| + |cot x – 9| + |cot x – 10| + |cot x – 11| + |cot x – 12| $$
Then find $x=operatorname{arcsec}(alpha/beta )$ where it is occurring.






calculus







share|cite|improve this question
























  • Done now what ?
    – D.Manek
    Nov 19 at 11:28













up vote
1
down vote

favorite









up vote
1
down vote

favorite











The global minimum value of
$$|cot x – 1| + |cot x – 2| + |cot x – 31| + |cot x – 32| + |cot x – 24| + |cot x – 5| + |cot x – 6|
+ |cot x – 17| + |cot x – 8| + |cot x – 9| + |cot x – 10| + |cot x – 11| + |cot x – 12| $$
Then find $x=operatorname{arcsec}(alpha/beta )$ where it is occurring.






calculus







share|cite|improve this question















The global minimum value of
$$|cot x – 1| + |cot x – 2| + |cot x – 31| + |cot x – 32| + |cot x – 24| + |cot x – 5| + |cot x – 6|
+ |cot x – 17| + |cot x – 8| + |cot x – 9| + |cot x – 10| + |cot x – 11| + |cot x – 12| $$
Then find $x=operatorname{arcsec}(alpha/beta )$ where it is occurring.






calculus




calculus






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edited Nov 19 at 11:36









amWhy

191k27223438




191k27223438










asked Nov 19 at 11:11









D.Manek

173




173












  • Done now what ?
    – D.Manek
    Nov 19 at 11:28


















  • Done now what ?
    – D.Manek
    Nov 19 at 11:28
















Done now what ?
– D.Manek
Nov 19 at 11:28




Done now what ?
– D.Manek
Nov 19 at 11:28










1 Answer
1






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3
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The minimum is achieved when $cot x$ is the median of the constants, i.e. $10$.



If $cot x=10$ then $sec x=dfrac{sqrt{101}}{10}$, which is not a rational number.






share|cite|improve this answer























  • why median but not mean?
    – idea
    Nov 19 at 11:37










  • can you kindly please explain me the whole thing I was unable to understand it.
    – D.Manek
    Nov 19 at 11:38












  • @idea The mean would be for the sum of squares.
    – Yves Daoust
    Nov 19 at 11:38












  • Why not try it both ways, @idea, and see what happens?
    – Gerry Myerson
    Nov 19 at 11:38










  • @D.Manek: do you know what the median is ?
    – Yves Daoust
    Nov 19 at 11:40











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1 Answer
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1






active

oldest

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up vote
3
down vote













The minimum is achieved when $cot x$ is the median of the constants, i.e. $10$.



If $cot x=10$ then $sec x=dfrac{sqrt{101}}{10}$, which is not a rational number.






share|cite|improve this answer























  • why median but not mean?
    – idea
    Nov 19 at 11:37










  • can you kindly please explain me the whole thing I was unable to understand it.
    – D.Manek
    Nov 19 at 11:38












  • @idea The mean would be for the sum of squares.
    – Yves Daoust
    Nov 19 at 11:38












  • Why not try it both ways, @idea, and see what happens?
    – Gerry Myerson
    Nov 19 at 11:38










  • @D.Manek: do you know what the median is ?
    – Yves Daoust
    Nov 19 at 11:40















up vote
3
down vote













The minimum is achieved when $cot x$ is the median of the constants, i.e. $10$.



If $cot x=10$ then $sec x=dfrac{sqrt{101}}{10}$, which is not a rational number.






share|cite|improve this answer























  • why median but not mean?
    – idea
    Nov 19 at 11:37










  • can you kindly please explain me the whole thing I was unable to understand it.
    – D.Manek
    Nov 19 at 11:38












  • @idea The mean would be for the sum of squares.
    – Yves Daoust
    Nov 19 at 11:38












  • Why not try it both ways, @idea, and see what happens?
    – Gerry Myerson
    Nov 19 at 11:38










  • @D.Manek: do you know what the median is ?
    – Yves Daoust
    Nov 19 at 11:40













up vote
3
down vote










up vote
3
down vote









The minimum is achieved when $cot x$ is the median of the constants, i.e. $10$.



If $cot x=10$ then $sec x=dfrac{sqrt{101}}{10}$, which is not a rational number.






share|cite|improve this answer














The minimum is achieved when $cot x$ is the median of the constants, i.e. $10$.



If $cot x=10$ then $sec x=dfrac{sqrt{101}}{10}$, which is not a rational number.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Nov 19 at 11:41

























answered Nov 19 at 11:36









Yves Daoust

122k668217




122k668217












  • why median but not mean?
    – idea
    Nov 19 at 11:37










  • can you kindly please explain me the whole thing I was unable to understand it.
    – D.Manek
    Nov 19 at 11:38












  • @idea The mean would be for the sum of squares.
    – Yves Daoust
    Nov 19 at 11:38












  • Why not try it both ways, @idea, and see what happens?
    – Gerry Myerson
    Nov 19 at 11:38










  • @D.Manek: do you know what the median is ?
    – Yves Daoust
    Nov 19 at 11:40


















  • why median but not mean?
    – idea
    Nov 19 at 11:37










  • can you kindly please explain me the whole thing I was unable to understand it.
    – D.Manek
    Nov 19 at 11:38












  • @idea The mean would be for the sum of squares.
    – Yves Daoust
    Nov 19 at 11:38












  • Why not try it both ways, @idea, and see what happens?
    – Gerry Myerson
    Nov 19 at 11:38










  • @D.Manek: do you know what the median is ?
    – Yves Daoust
    Nov 19 at 11:40
















why median but not mean?
– idea
Nov 19 at 11:37




why median but not mean?
– idea
Nov 19 at 11:37












can you kindly please explain me the whole thing I was unable to understand it.
– D.Manek
Nov 19 at 11:38






can you kindly please explain me the whole thing I was unable to understand it.
– D.Manek
Nov 19 at 11:38














@idea The mean would be for the sum of squares.
– Yves Daoust
Nov 19 at 11:38






@idea The mean would be for the sum of squares.
– Yves Daoust
Nov 19 at 11:38














Why not try it both ways, @idea, and see what happens?
– Gerry Myerson
Nov 19 at 11:38




Why not try it both ways, @idea, and see what happens?
– Gerry Myerson
Nov 19 at 11:38












@D.Manek: do you know what the median is ?
– Yves Daoust
Nov 19 at 11:40




@D.Manek: do you know what the median is ?
– Yves Daoust
Nov 19 at 11:40


















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