Since relative minimum is located at point (-3 , -18) and relative maximum is located at point (1/3, 14/27), then the function is:
1. strictly decreasing for [tex]x\in (-\infty, -3)\cup ( \frac{1}{3}, \infty )[/tex] and decreasing for [tex]x\in (-\infty, -3]\cup [\frac{1}{3}, \infty )[/tex]
2. strictly increasing for [tex]x\in (-3, \frac{1}{3} )[/tex] and increasing for [tex]x\in [-3, \frac{1}{3} ][/tex] .
Hence all points with [tex]x\in (-\infty, -3]\cup [\frac{1}{3}, \infty )[/tex] are located where the graph of f(x) is decreasing. There are points (2, -18), (1, -2), (-3,-18) and (-4, -12). Check if they sutisfy the function expression:
1. [tex]f(2)= -2^3 - 4\cdot 2^2 + 3\cdot 2=-8-16+6=-18[/tex];
2. [tex]f(1)= -1^3 - 4\cdot 1^2 + 3\cdot 1=-1-4+3=-2[/tex];
3. [tex]f(-4)= -(-4)^3 - 4\cdot (-4)^2 + 3\cdot (-4)=64-64-12=-12[/tex].
Note that point (-3, -18) is a turning point.
Answer: ordered pairs (2, -18), (1, -2) and (-4, -12) are located where the graph of f(x) is strictly decreasing and (-3,-18) is located where the graph of f(x) is decreasing.
