 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2015/paper-2/3/solution

lo g (1 + x^{2}) = x^{2} - \frac{x ^{4}}{2} + O (x^{6}) .

The first nonzero term is therefore

x^{2}

. It is positive on either side of the origin, so the stationary point is a strict local minimum. In fact

lo g (1 + x^{2}) \geq 0

, with equality only at zero, making it the global minimum as well.

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