Find all the points of local maxima and local minima of the function $f$ given by $f(x) = 2x^3 - 6x^2 + 6x + 5$.

(NONE) Given the function $f(x) = 2x^3 - 6x^2 + 6x + 5$.
First,we find the first derivative: $f'(x) = 6x^2 - 12x + 6 = 6(x^2 - 2x + 1) = 6(x - 1)^2$.
Setting $f'(x) = 0$,we get $6(x - 1)^2 = 0$,which implies $x = 1$.
Now,we examine the sign of $f'(x)$ around $x = 1$.
For $x < 1$,$(x - 1)^2 > 0$,so $f'(x) > 0$.
For $x > 1$,$(x - 1)^2 > 0$,so $f'(x) > 0$.
Since the sign of $f'(x)$ does not change as $x$ passes through $1$ (it remains positive on both sides),the function $f(x)$ is strictly increasing at $x = 1$.
Therefore,$x = 1$ is neither a point of local maxima nor a point of local minima. It is a point of inflexion.