determine the intervals in which the following polynomial is increasing and decreasing: (-2.17,-1.18)…

Explanation:

Step1: Recall the definition of increasing and decreasing functions

A function (y = f(x)) is increasing on an interval if for any two points (x_1) and (x_2) in the interval with (x_1<x_2), (f(x_1)<f(x_2)). A function is decreasing on an interval if for any two points (x_1) and (x_2) in the interval with (x_1 < x_2), (f(x_1)>f(x_2)).

Step2: Analyze the graph

• For the interval ((-\infty,-4)): As (x) increases (moves from left to right), the (y -) values of the function decrease.
• For the interval ((-4, - 2.17)): As (x) increases (moves from left to right), the (y -) values of the function increase.
• For the interval ((-2.17,0.92)): As (x) increases (moves from left to right), the (y -) values of the function decrease.
• For the interval ((0.92,\infty)): As (x) increases (moves from left to right), the (y -) values of the function increase.

Answer:

The function is increasing on the intervals ((-4,-2.17)) and ((0.92,\infty)), and decreasing on the intervals ((-\infty,-4)) and ((-2.17,0.92))