2009 Indonesia MO Problems/Problem 6
Revision as of 11:40, 31 August 2018 by Rockmanex3 (talk | contribs) (Solution to Problem 6 (credit to wangsacl) -- Calculus!!!)
Problem
Find the lowest possible values from the function
for any real numbers
.
Solution
We start the search for potential minimums by taking the derivative of and setting it to equal 0.
Notice from the symmetry of the function that
. This makes
a possible minimum of the function.
To check, we find that
From the Trivial Inequality,
and
, so
. Thus, the minimum of
is
, obtained when
.
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
See Also
2009 Indonesia MO (Problems) | ||
Preceded by Problem 5 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 | Followed by Problem 7 |
All Indonesia MO Problems and Solutions |