Determine maximum value of a 4th order polynomial function with two variables

Kikookik

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Aug 19, 2017
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Hello
I would like to know the maximum and the minimum of a 4th order polynomial function P(a,b) of two variables a and b, where a, b are real positive numbers.
P(a,b) = a4 + 8a3b + 12a2b2 + 8ab3
There is a condition is that the quantity a2 + 4ab is always constant.

So how to solve that type of problem, I know a solution to a similar problem already exist somewhere on the internet so can someone here please give a link to such solution or procedure.

Thank You
 
Hello
I would like to know the maximum and the minimum of a 4th order polynomial function P(a,b) of two variables a and b, where a, b are real positive numbers.
P(a,b) = a4 + 8a3b + 12a2b2 + 8ab3
There is a condition is that the quantity a2 + 4ab is always constant.

So how to solve that type of problem, I know a solution to a similar problem already exist somewhere on the internet so can someone here please give a link to such solution or procedure.

Thank You
what are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33
 
Sorry, if I post in the wrong section or maybe the wrong forum either. Just was using Google to search for a forum that help with mathematical problems and found this one, but it seem that my destination was wrong. Sorry again and just remove that topic if you fell unconformable or if it take some disk space in your database.
Good bye.
 
… polynomial function P(a,b) of two variables a and b

… the quantity a2 + 4ab is always constant
If the expression a^2 + 4ab represents a constant, then symbols a and b are not variables.
 
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