2009 Indonesia MO Problems/Problem 6
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 |