1983 AIME Problems/Problem 2
Problem
Let , where
. Determine the minimum value taken by
for
in the interval
.
Solution
It is best to get rid of the absolute values first.
Under the given circumstances, we notice that ,
, and
.
Adding these together, we find that the sum is equal to , which attains its minimum value (on the given interval
) when
, giving a minimum of
.
See Also
1983 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |