 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2007/paper-1/section-a/10/a/solution

The function is nonnegative and satisfies

cos^{2} (π - x) = cos^{2} x

- sin (2 x)

, so it decreases from

(0, 1)

to its minimum

(π /2, 0)

and then increases to

(π, 1)

. These three points all have horizontal tangent lines.

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