Multivariate Optimisation

[mathshelpplease]

Hello,

I have been trying to solve this problem:



And have come up with the solution



But, when I checked my answer through a graphing simulator, I found these maximum and saddle points to be wrong.




Can anyone help by pointing out where I have made a mistake?

Thank you.

 

[blamocur]

I got the same answers as you. As for your graph, I cannot analyze it so I've built my own(attached), and it looks fine to me.

 

[mathshelpplease]

I got the same answers as you. As for your graph, I cannot analyze it so I've built my own(attached), and it looks fine to me.

Thank you for your reply, I was wondering if it is because the real numbers provision at the start? would this mess up the results?

 

[blamocur]

Thank you for your reply, I was wondering if it is because the real numbers provision at the start? would this mess up the results?

But the numbers in the solutions are real. Why would this mess up the results?

 

[mathshelpplease]

But the numbers in the solutions are real. Why would this mess up the results?

Sorry you are completely correct, I mixed up real with rational for a second. Thank you for your help.