# 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, 5 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

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

- 4 years, 5 months ago

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

- 4 years, 5 months ago