= Solution
A <stationary point> occurs where the <derivative> vanishes. Here
$$
f'(x)=6+12\sin(3x)=0\quad\Longleftrightarrow\quad\sin(3x)=-\frac12.
$$
The two families are
$$
\boxed{x=\frac{7\pi}{18}+\frac{2n\pi}{3}\quad\text{or}\quad x=\frac{11\pi}{18}+\frac{2n\pi}{3},\qquad n\in\mathbb Z.}
$$
Consequently there are \b[infinitely many] <stationary points> on the real line. The second <derivative> is $36\cos(3x)$: the first family consists of strict <local minima> and the second of strict <local maxima>.
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