 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2018/paper-1/8/solution

y^{'} = e^{x} (cos x - sin x)

tan x = 1

. In the given interval this means

x = π /4

. Substitution gives

(x, y) = (\frac{π}{4}, \frac{e ^{π /4}}{2}) .

The derivative changes from positive to negative there, making it a strict local maximum.

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