Math Problem Statement
List the intervals where f is decreasing
Solution
To determine where the function is decreasing, we need to observe the intervals on the graph where the slope of the curve is negative, meaning the function is sloping downwards as we move from left to right.
From the graph you provided:
- The function is decreasing from approximately to (left side of the curve as it moves downward).
- The function starts decreasing again from to (right side of the curve after it reaches its peak at ).
So, the intervals where is decreasing are:
Would you like further details or have any questions about this?
Here are 5 related questions for practice:
- What are the intervals where the function is increasing?
- Can you identify the relative minimum and maximum points?
- What is the value of at ?
- How would you estimate the average rate of change of the function between and ?
- What kind of symmetry does this function exhibit, if any?
Tip: To determine if a function is increasing or decreasing, always check the sign of the derivative or visually inspect where the graph slopes up or down!
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Math Problem Analysis
Mathematical Concepts
Calculus
Graphing
Rates of Change
Formulas
Interval notation for increasing/decreasing functions
Derivative of f(x) to find intervals of increasing or decreasing
Theorems
First Derivative Test
Suitable Grade Level
Grades 10-12