1952 AHSME Problems/Problem 13
Problem
The function with and greater than zero has its minimum value when:
Solution
The minimum value of this parabola is found at its turning point, on the line . Indeed, the turning point of any function of the form has an x-coordinate of . This can be seen at the average of the quadratic's two roots (whose sum is ) or (using calculus) as the value of its derivative set equal to .
See also
1952 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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