TMUA 2017 · Paper 1 · Question 16

The functions $f$ and $g$ are given by $f (x) = 3 x^{2} + 12 x + 4$ and $g (x) = x^{3} + 6 x^{2} + 9 x - 8$ .

What is the complete set of values of $x$ for which one of the functions is increasing and the other decreasing?