Question

Pls help fast (algebra 2)

Use a graph of the polynomial
function f(x) = -x4 - 4x³ - x² + 6x to
complete the sentences.
positive negative) (increasing
decreasing
on the intervals
fis
(-3, -2) and (0, 1).
fis increasing on the intervals
(-∞, -3), (-2, 0), and (1, ∞).
fis
on the intervals
(-2.6, -1) and (0.6, ∞).

Answer 1

The polynomial function f(x) is positive on the intervals (-3, -2) and (0, 1), and it is increasing on the intervals (-∞, -3), (-2, 0), and (1, ∞). Without additional context or a graph, it is impossible to definitively conclude the behavior on other intervals, but f(x) is implied to be decreasing on the intervals (-2.6, -1) and (0.6, ∞).

Step-by-step explanation:

To analyze the given polynomial function f(x) = -x4 - 4x3 - x2 + 6x, we look for intervals where the function is increasing or decreasing and where it is positive or negative.

To determine these intervals, we typically use calculus techniques (finding derivatives and solving for critical points) or by creating a sign chart. However, in this case, it seems the information provided already outlines the intervals of increase and decrease.

The function is described as positive on the intervals (-3, -2) and (0, 1), which means f(x) > 0 for x values in these intervals. Moreover, the function is increasing on the intervals (-∞, -3), (-2, 0), and (1, ∞). This highlights that the function's output is getting larger as x moves through these intervals.

Lastly, since the last sentence of the description is not complete, based on the previous information, we can deduce that the function would be decreasing on the intervals (-2.6, -1) and (0.6, ∞), although this cannot be confirmed without the full context or a graph.