1983 AIME Problems/Problem 2
Contents
[hide]Problem
Let , where . Determine the minimum value taken by for in the interval .
Solution
Solution 1
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 .
Solution 2
Let be equal to , where is an almost neglectable value. Because of the small value , the domain of is basically the set . plugging in gives , or , so the answer is
See Also
1983 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
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All AIME Problems and Solutions |