2027학년도 고3 6월 모의고사 수학 21번

Question 21 (4 points) from the June Mock Exam for High School Seniors, involving a cubic function f(x) and its derivative f′(t). The function f(x) is completely determined by a single condition: that the maximum root g(t) of the equation f(α) = f′(t) − 4t² + 4 is discontinuous "at only one point." You absolutely cannot solve this if you get stuck in the swamp of formulas. The key is a single line of graph intuition: "The maximum root jumps sharply the moment the horizontal line passes the minimum value." Even a Grade 4 student can solve Question 21 if they grasp this one sentence. 📌 What You Learn in This Video · The perspective of viewing the right-hand side f′(t) − 4t² + 4 as a 'height (constant) independent of α' · The reason why the discontinuity of the maximum root g(t) occurs only at the 'moment of passing the minimum value' · Only one discontinuity → Interpretation that the upward-convex parabola 'tangentially' the minimum value · The solution flow of determining the coefficients a, b, and c in order from the minimum point g(3)=1 🎯 [Problem] A cubic function f(x) with a leading coefficient of 1. For a real number t, Let g(t) be the maximum value of the real number α that satisfies f(α) = f′(t) − 4t² + 4 When the function g(t) is discontinuous only at t = 3 and g(3) = 1, find the value of f(2). ────────────── 101 MATH is a 'lecture' channel that captures 20 years of offline teaching expertise. It doesn't stop at just a taste of shorts — we cover a problem from start to finish.. Where the joy of learning translates into high scores. 101 MATH ▶ Subscribe and check out the High School Senior problems first!! #HighSchoolSeniorMath #JuneMockExam #CubicFunction #DifferentiationOfPolynomialFunctions #ContinuityOfFunctions #CSATMath #MockExamSolutions #NearKillerProblems #101MATH #OnlineMathLecture