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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 15 Consider the function f(x) = ( −x2 (x <0), x2 −x(x≥0), and, for a positive real numbera, define the function g(x) = ax+a(x <−1), 0 (−1≤x <1), ax−a(x≥1). Define h(x) = Z x 0 � g(t)−f(t) dt. Letkbe the maximum value ofafor which the functionh(x) has exactly one extremum (local maximum or local minimum). Whena=k, compute the value ofk+h(3). [4 points] ① 9 2 ② 11 2 ③ 13 2 ④ 15 2 ⑤ 17 2 6 Numerical answer
\boxed{④}
Comparative Analysis (P14) (Average across runs)
Averages use reported measurements only. Missing usage is not treated as zero.