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# These statement are often quoted as fact. But are they true?

Statement 1. $$f(x,y)$$ is a function that is cyclic in the variables, does this mean that subject to $$x+y = 1$$, the local minimum or maximum can only occur at $$f( \frac{1}{2}, \frac{1}{2} ) ?$$

Statement 2. $$f(x,y,z)$$ is a function that is cyclic in the variables, does this mean that subject to $$x + y + z = 1$$, the local minimum or maximum can only occur at $$f( \frac{1}{3}, \frac{1}{3}, \frac{1}{3} )$$?

Note by Chung Kevin
4 years ago

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For counterexamples, take $f(x,y)=xy$ and $f(x,y,z)=xyz$

- 4 years ago

I've updated it slightly, to get at the original intention.

- 4 years ago

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