 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-1/8/b/solution

y^{''} = 6 x

, so

y^{''} (1) = 6 > 0

. By the second-derivative test, the stationary point is a strict local minimum, at

(1, 5)

. It is not a global minimum, since this cubic is unbounded below toward negative infinity.

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