# (easier version)What is a working example for finding the maximum of a algebraic function $f(a,b,c,d,e)$ with 4 equality …

edit 2: If you are founding an answer would be interesting to you, please upvote this question, because i may use those point in order to start a new bounty.

Edit 4:I have been thinking this about for a month, but generating nothing, can somebody answer this?

## edit 3: The 100 point bounty is already end, so following the rules, i have to create a 200 points bounty. If you love this question, please upvote my question and show some support by answering.

This is the easier version of this problem:

What is a working example and a non-working for finding the maximum of a special function $f(a,b,c,d,e)$ with 4 equality / inequality constraints?

problem no. 50: Part a) What is the general method to find all the maximum/minimum of a algebraic equation and a working example for finding the maximum of a algebraic function $f(a,b,c,d,e)$ with 4 constraints?

If there is no finite numbers of method to solve all maximization problems." rigourously and formally?

The function itself can either be a non-linear algebraic function. Each nonlinear algebraic(no linear here) constraints and must use more than one variable and are some inequality (appear more than 1 times) and some equality(appear more than 1 time). Assuming there are no closed form at the end, could you provide the exact infinite sum method?

E.g. I could just take $f(x,y,z,t,s) = 1-x^2-y^2-z^2-t^2-s^2$. Take the constraints $x^2+y^2 = 0, y^2 + z^2 =0, z^2 + t^2 \leq 1, t^2 + s^2 \leq 1$. Then the maximum is clearly at $x=y=z=t=s=0$. But I don't think this is what you are looking for. I recommend cleaning up your question and being more specific about what you want. – nullUser Oct 1 '12 at 21:11
if you are referring to the example I gave in my comment above, yes I can. Note that $-x^2-y^2-z^2-t^2-s^2$ is a nonpositive quantity. It follows that $f(x,y,z,t,s) \leq 1$. Plug in all zeros and you get $f(x,y,z,t,s) = 1$. Note that all zeros satisfy the constraints as well. It follows that this is a global maximum of $f$. – nullUser Oct 1 '12 at 21:23