Multivariate Optimization and Area/Volume homework check

[Liquid7800]

Homework Statement

Hello,

If you don’t mind, would you all be able to look over these problems for me? I have left out much of the ‘algebra’ work for the sake of space…so please let me know if you think there are any algebra errors.

In addition I am particularly looking to see if I have set up these problems correctly and understand what is going on with them---For number 7, I was told by a classmate that I am missing two more critical points and don't have all the possible combinations
...I am not sure what he means as I think I have followed all the necessary steps to get the criticial numbers, if I left out a step please let me know.

Ques1.
DISREGARD

Ques.3
DISREGARD

Ques 4.
DISREGARD

Ques. 5

Ques. 7

I have scanned in these problem ‘sketches’…so please let me know if you cannot see them.

I appreciate your time and help as always.

 

[Mark44]

Five pages is a lot for anyone to look through. IMO, it would be better if you posted these separately.

 

[Liquid7800]

I am sorry Mark...I guess I didnt realize how difficult these might actually be for you all to check over.

I have taken down a couple in response,...I will take this into consideration in the future for other homework checks

...if anyone would like to take a stab at at least one...please look at number 7.

 

[Dick]

I am sorry Mark...I guess I didnt realize how difficult these might actually be for you all to check over.

I have taken down a couple in response,...I will take this into consideration in the future for other homework checks

...if anyone would like to take a stab at at least one...please look at number 7.

Regarding number 7, why do you get only two critical points? Looks to me like you should have four.

 

[Liquid7800]

Thanks for the reply Dick...however, all I can say is maybe regarding the polynomials for Fx and Fy
x=0 and y=0 as well?, thus getting another critical point (0,0)? But I don't see how to find four though?
I feel I am missing something here.

 

[Dick]

Thanks for the reply Dick...however, all I can say is maybe regarding the polynomials for Fx and Fy
x=0 and y=0 as well?, thus getting another critical point (0,0)? But I don't see how to find four though?
I feel I am missing something here.

Noo. You've got Fx and Fy fine and their solutions fine. So you have two x values where the Fx derivative vanishes and two y values where the Fy derivative vanishes. Doesn't that give you four points in the xy plane where both vanish??! What about x=(-1) and y=(-1)? Did you just leave that out because you dislike that point?

 

[Liquid7800]

So you have two x values where the Fx derivative vanishes and two y values where the Fy derivative vanishes. Doesn't that give you four points in the xy plane where both vanish??! What about x=(-1) and y=(-1)?

Let me see, by this hint I should also have (-1,-1) and (-5,3) as well as (-1,3) and (-5,-1)
as these are the total possible combination's of the four points on this xy plane?

 

[Dick]

Let me see, by this hint I should also have (-1,-1) and (-5,3) as well as (-1,3) and (-5,-1)
as these are the total possible combination's of the four points on this xy plane?

Well, sure. You've got two vertical lines where Fx vanishes and two horizontal lines where Fy vanishes. Four intersection points, yes?

 

[Liquid7800]

Thanks Dick,
Its always the little stuff that gets me, thanks for the explanation---I don't know how I missed that either in hindsight