API · no tools. This is the prompt and response recorded for this attempt; a full solution may not have been returned.
Problem Statement
This is a Korean CSAT mathematics multiple-choice problem. Solve it and put only the correct choice symbol, one of ①, ②, ③, ④, ⑤, inside \boxed{}.
Problem 9 For a positive real numbera, define f(x) =x 3 + 3ax2 −9a 2x+ 4. Suppose that the liney= 5 is tangent to the curvey=f(x). Determine the value of f(2). [4 points] 3 ①11 ②12 ③13 ④14 ⑤15
Ground Truth
④
Recorded model response / solution
Reasoning Process
\boxed{④}
Final Model Output
④
Comparative Analysis (P8) (Average across runs)
Averages use reported measurements only. Missing usage is not treated as zero.
Avg Time Taken
Motif 3
27.7
Solar Pro 4
24.0
Kimi K3
10.8
K-EXAONE-2
2.0
Avg Token Usage
Solar Pro 4
1196.0
K-EXAONE-2
910.0
Kimi K3
872.3