 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-1/4/a/solution

f^{'} (x) = \frac{2 x}{a ^{2}} - \frac{2 a ^{2}}{x ^{3}} .

x = 1

requires

2/ a^{2} - 2 a^{2} = 0

, or

a^{4} = 1

. Since

a > 0

a = 1

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