Solution
(a) setting f(x) = 0
[tex]\begin{gathered} 3x^4-18x^3-21x^2+144x-108=0 \\ \\ (x+3)(x-1)(x-2)(x-6)=0 \\ \\ \Rightarrow x=-3,1,2,6 \end{gathered}[/tex]
(b)
when x = 0
y = f(0) = -108
Hence, the height is 108
(c)
Maximum = (1.5, 15.188)
(d)
Minimum (-1.702, -300) and (4.702, -300)
(e) From the graph, the interval of increasing is
[tex]\begin{gathered} (-1.7,\frac{3}{2}),(4.7,\infty) \\ \end{gathered}[/tex]
(f) From the graph, the interval of decreasing is;
[tex](-\infty,-1.7),(\frac{3}{2},4.7)[/tex]
g)
