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 numerical-answer problem. Solve it and put only the final integer value inside \boxed{}.
Problem 19 For all real numbersxwith−2≤x≤2, the inequality −k≤2x 3 + 3x2 −12x−8≤k holds. Find the smallest possible positive value ofk. [3 points]
Ground Truth
15
Recorded model response / solution
Reasoning Process
\boxed{15}
Final Model Output
15
Comparative Analysis (P18) (Average across runs)
Averages use reported measurements only. Missing usage is not treated as zero.
Avg Time Taken
Motif 3
13.7
Solar Pro 4
12.8
Kimi K3
11.7
K-EXAONE-2
1.5
Avg Token Usage
Solar Pro 4
931.3
K-EXAONE-2
625.3
Kimi K3
524.3