 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2011/paper-2/9/solution

d y / d x = 3 x^{2}

, giving slope twelve at

x = 2

. The point on the curve is

(2, 9)

. The point-slope equation of the tangent line is consequently

y - 9 = 12 (x - 2), y = 12 x - 15 .

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