Question 47: The maximum point of the graph of the function (y = 2{x^3} – 6x + 1) is

We have:

\(\begin{array}{l}’ = 6{x^2} – 6 = 0 \Leftrightarrow x = \pm 1.\\y” = 12x,\,y”\left( { – 1} \ right) = – 12 < 0,y”\left( 1 \right) = 12 > 0\end{array}\)

So the maximum point of the graph of the function is x = – 1.