Problem:
Given that −4≤x≤−2 and 2≤y≤4, what is the largest possible value of xx+y​?
Answer Choices:
A. −1
B. −21​
C. 0
D. 21​
E. 1
Solution:
Because
xx+y​=1+xy​ and xy​<0
the value is maximized when ∣y/x∣ is minimized, that is, when ∣y∣ is minimized and ∣x∣ is maximized. So y=2 and x=−4 gives the largest value, which is 1+(−1/2)=21​.
Answer: D​.
The problems on this page are the property of the MAA's American Mathematics Competitions