Question 23: The maximum point of the graph of the function (y = {x^3} + 3{x^2} + 2) is

We have \(y’ = 3{x^2} + 6x\).

Then: \(y’ = 0 \Leftrightarrow 3{x^2} + 6x = 0 \Leftrightarrow \left[\begin{array}{l}x=0\\x=–2\end{array}\right\)[\begin{array}{l}x=0\x=–2\end{array}\right\)

We have a variable table:

So the maximum point of the function graph has coordinates \(\left( { – 2;\,6} \right)\)