Question

Consider the function below, which has a relative minimum located at (-3 , -18) and a relative maximum located at (1/3, 14/27)

f(x) = -x^3 - 4x^2 + 3x

Select all ordered pairs in the table which are located where the graph of f(x) is decreasing.

(-1, -6)
(2, -18)
(0, 0)
(1, -2)
(-3, -18)
(-4, -12)

Answer 1

PIECE OF ADVICE. this could be stupid and all yall might just be like 'yeah we know okay we're not dumb' but the other person is right, however, DONT PUT (-3, -18) IN YOUR ANSWER. sorry just felt like i needed to clarify that a little.

Explanation:

I hope this helps a little bit :))

Answer 2

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
`x\in (-\infty, -3)\cup ( (1)/(3), \infty )` and decreasing for
`x\in (-\infty, -3]\cup [(1)/(3), \infty )`

2. strictly increasing for
`x\in (-3, (1)/(3) )` and increasing for
`x\in [-3, (1)/(3) ]` .

Hence all points with
`x\in (-\infty, -3]\cup [(1)/(3), \infty )` 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.
`f(2)= -2^3 - 4\cdot 2^2 + 3\cdot 2=-8-16+6=-18`;

2.
`f(1)= -1^3 - 4\cdot 1^2 + 3\cdot 1=-1-4+3=-2`;

3.
`f(-4)= -(-4)^3 - 4\cdot (-4)^2 + 3\cdot (-4)=64-64-12=-12`.
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.