https://file.aiquickdraw.com/mathbot/file/1726707449378qtdyniqv.jpg

To solve this, we need to analyze the graph and determine where the rate of change (or slope) of the function is increasing.

### Steps:
1. **Interpret the Graph**: The graph appears to have a curve that changes direction, so we are looking for intervals where the slope becomes more positive or less negative.

2. **Focus on the Slope**: Rate of change refers to the derivative of the function, i.e., the slope of the tangent line at any point on the curve. Where the slope is increasing, the graph curves upwards.

3. **Identifying the Increasing Interval**:
   - For \(x < 2\), the graph slopes downward, and the curve is concave down (decreasing slope).
   - After \(x = 2\), the curve changes and becomes concave up. The slope is negative at \(x = 2\), but as \(x\) increases beyond 2, the slope becomes less negative and eventually positive. This indicates that the rate of change is increasing for \(x > 2\).

### Conclusion:
The rate of change is increasing in the interval \((2, \infty)\). This corresponds to the answer:
- **(2, ∞)**

Do you have any questions or would you like a detailed explanation of any part?

### Related Questions:
1. What is the derivative of a function, and how does it relate to the slope of a curve?
2. How can you determine concavity and inflection points from a graph?
3. What is the difference between increasing and decreasing intervals on a function's graph?
4. How would the graph look if the rate of change were decreasing?
5. How can you find the intervals of increase and decrease algebraically?

### Tip:
When analyzing rate of change, remember that concave up curves indicate increasing slope, and concave down curves indicate decreasing slope.

Find the intervals of the function graphed below where the rate of change is increasing.

This problem focuses on identifying the intervals where the rate of change of a function is increasing based on the graph's concavity. It covers key calculus concepts like the first and second derivative tests and is suitable for students in Grades 11-12.

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