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:
- The function decreases from to .
- The function then decreases again from to .
Thus, the correct intervals where the function is decreasing match the second option:
- and
Would you like any further explanation?
Here are some related questions you might consider:
- How can we use derivatives to confirm where a function is increasing or decreasing?
- What are the critical points, and how do they relate to increasing/decreasing intervals?
- Can you determine concavity from the graph of a function?
- What is the significance of inflection points in the behavior of a function?
- 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.
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Math Problem Analysis
Mathematical Concepts
Inequalities
Formulas
-
Theorems
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Suitable Grade Level
High School
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