To determine where the average rate of change of the function \( f(x) \) is positive, we need to analyze how the function behaves across given intervals. The average rate of change of a function on the interval \([a, b]\) is defined as:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
This expression is positive if \( f(b) > f(a) \) for the selected interval \([a, b]\).
Without the actual graph to analyze, I can't identify the specific behavior of \( f(x) \) in the intervals provided. However, you can check the graph by looking at the values of \( f(x) \) at the endpoints of each interval:
- For the interval \([0, 2]\): Check \( f(2) \) and \( f(0) \).
- For the interval \([2, 3]\): Check \( f(3) \) and \( f(2) \).
- For the interval \([0, 4]\): Check \( f(4) \) and \( f(0) \).
- For the interval \([0, 5]\): Check \( f(5) \) and \( f(0) \).
You should identify which of these intervals results in \( f(b) > f(a) \). Pick the option that corresponds with which of these intervals displays a positive slope (i.e., \( f(x) \) is increasing).
Try to analyze the graph based on these principles, and you should be able to determine the correct interval where the average rate of change is positive. If you can provide more details about the graph or its behavior, I'd be able to assist further!