Answer
$${\text{no maximum or minimum}}$$
Work Step by Step
$$\eqalign{
& f\left( x \right) = 2{x^3} - 6x + 2;\,\,\left( { - \infty , + \infty } \right) \cr
& {\text{The function is a polynomial }} \cr
& {\text{Since }}f(x){\text{ has odd }}\,{\text{degree we have that}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\mathop {\lim }\limits_{x \to + \infty } f\left( x \right){\text{ and }}\mathop {\lim }\limits_{x \to - \infty } f\left( x \right) \cr
& {\text{have opposite signs }}\left( {{\text{one is + }}\infty {\text{ and the other is }} - \infty } \right),{\text{ so there are no}} \cr
& {\text{absolute extrema}}{\text{.}} \cr} $$