Question

determine the intervals in which the following polynomial is increasing and decreasing: (-2.17,-1.18) (-4,-2) (0.92,-4.51) (-∞,-4) (-4,-2.17) (-2.17,0.92) (0.92,∞)

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

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 \((-2.17,0.92)\)