 Solution

ID: past-exam-of-the-mathematical-methods-ii-course-of-the-university-of-oxford/2021/1/ii/solution

f^{'} (x) = 10 e^{3 - x^{2}} (1 - 2 x^{2}) .

The exponential function is strictly positive, so there are exactly two stationary points, at

x = \pm 1/ 2

. The derivative is negative outside these two values and positive between them. Thus the negative value is a strict local minimum and the positive value a strict local maximum.

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