2006 Cyprus MO/Lyceum/Problem 4
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Problem
Given the function 
, 
Which of the following is correct, about the graph of 
?
Solution
Notice that if 
, then 
has the unique root of 
, so it touches the x-axis, 
.
From above, 
is not correct because the graph does not intersect the x-axis (it is tangent to it).
is not true; the graph intersects the y-axis since the parabola opens up or down.
and 
depend upon the value of 
; if 
, then the parabola has a minimum, and if then the parabola has a maximum.
Thus, the answer is .
See also
| 2006 Cyprus MO, Lyceum (Problems) | ||
| Preceded by Problem 3 | Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
