Let's find the inflection points, we'll need to solve the equation for this
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$
the second derivative$$\frac{1 - \frac{3}{\log{\left(x^{3} \right)}}}{x \log{\left(x^{3} \right)}} = 0$$
Solve this equationThe roots of this equation
$$x_{1} = e$$
Сonvexity and concavity intervals:Let’s find the intervals where the function is convex or concave, for this look at the behaviour of the function at the inflection points:
Concave at the intervals
$$\left[e, \infty\right)$$
Convex at the intervals
$$\left(-\infty, e\right]$$