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
edited Nov 19 at 11:36
amWhy
191k28223439
asked Nov 19 at 11:11
D.Manek
173
add a comment |
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
edited Nov 19 at 11:36
amWhy
191k28223439
asked Nov 19 at 11:11
D.Manek
173
Done now what ?
– D.Manek
Nov 19 at 11:28
add a comment |
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
edited Nov 19 at 11:36
amWhy
191k28223439
asked Nov 19 at 11:11
D.Manek
173
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
edited Nov 19 at 11:36
amWhy
191k28223439
asked Nov 19 at 11:11
D.Manek
173
edited Nov 19 at 11:36
amWhy
191k28223439
asked Nov 19 at 11:11
D.Manek
173
edited Nov 19 at 11:36
amWhy
191k28223439
edited Nov 19 at 11:36
amWhy
191k28223439
edited Nov 19 at 11:36
amWhy
191k28223439
191k28223439
asked Nov 19 at 11:11
D.Manek
173
asked Nov 19 at 11:11
D.Manek
173
asked Nov 19 at 11:11
D.Manek
173
173
Done now what ?
– D.Manek
Nov 19 at 11:28
add a comment |
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
add a comment |
1 Answer
1
active
oldest
votes
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.
answered Nov 19 at 11:36
Yves Daoust
123k668219
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
|
show 7 more comments
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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.
answered Nov 19 at 11:36
Yves Daoust
123k668219
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
|
show 7 more comments
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.
answered Nov 19 at 11:36
Yves Daoust
123k668219
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
|
show 7 more comments
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.
answered Nov 19 at 11:36
Yves Daoust
123k668219
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.
answered Nov 19 at 11:36
Yves Daoust
123k668219
edited Nov 19 at 11:41
answered Nov 19 at 11:36
Yves Daoust
123k668219
answered Nov 19 at 11:36
Yves Daoust
123k668219
answered Nov 19 at 11:36
Yves Daoust
123k668219
123k668219
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
|
show 7 more comments
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
|
show 7 more comments
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Done now what ?
– D.Manek
Nov 19 at 11:28