Math Problem Statement

-3<x<2

x>-3 and x<-0.5

x<-3 and x>-0.5

x>5

Solution

Given these new options, let's analyze the intervals where the function is decreasing.

Looking at the graph:

  1. The function decreases from x=3x = -3 to x=0.5x = -0.5.
  2. The function then decreases again from x=3x = 3 to x=5x = 5.

Thus, the correct intervals where the function is decreasing match the second option:

  • x>3x > -3 and x<0.5x < -0.5

Would you like any further explanation?

Here are some related questions you might consider:

  1. How can we use derivatives to confirm where a function is increasing or decreasing?
  2. What are the critical points, and how do they relate to increasing/decreasing intervals?
  3. Can you determine concavity from the graph of a function?
  4. What is the significance of inflection points in the behavior of a function?
  5. How can you identify points of inflection from the first derivative?

Tip: When determining where a function is decreasing, always consider the behavior of the function as it moves from left to right across the x-axis.