 Solution

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

A stationary point occurs where the derivative vanishes. Here

f^{'} (x) = 6 + 12 sin (3 x) = 0 ⟺ sin (3 x) = - \frac{1}{2} .

The two families are

x = \frac{7 π}{18} + \frac{2 nπ}{3} or x = \frac{11 π}{18} + \frac{2 nπ}{3}, n \in Z .

Consequently there are infinitely many stationary points on the real line. The second derivative is

36 cos (3 x)

 New to topics? Read the docs here!