2006 Cyprus MO/Lyceum/Problem 4
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 | |
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