Difference between revisions of "1983 AIME Problems/Problem 2"
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Adding these together, we find that the sum is equal to <math>30-x</math>, of which the minimum value is attained when <math>x=15</math>. | Adding these together, we find that the sum is equal to <math>30-x</math>, of which the minimum value is attained when <math>x=15</math>. | ||
− | The answer is thus <math> | + | The answer is thus <math>15</math>. |
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Revision as of 22:49, 23 July 2006
Problem
Let , where . Determine the minimum value taken by by in the interval .
Solution
It is best to get rid of the absolute value first.
Under the given circumstances, we notice that , , and .
Adding these together, we find that the sum is equal to , of which the minimum value is attained when .
The answer is thus .