 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/a/solution

Differentiate the polynomial and factor:

y^{'} = 3 x^{2} - 4 x - 7 = (3 x - 7) (x + 1) .

The stationary points therefore have horizontal coordinates

x = - 1, x = 7/3.

For a check,

y^{''} = 6 x - 4

is negative at the first and positive at the second, giving a local maximum and a local minimum respectively.

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