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The problem asks for the **instantaneous rate of change** of the graph at \( x = 1 \), which is essentially asking for the **slope of the tangent line** at that point.

Looking at the graph:

- The point \( x = 1 \) is located on the downward curve of the graph.
- Estimating the slope, the tangent line at \( x = 1 \) appears to have a negative slope, which matches the value you've written, \( -2 \).

Thus, the **instantaneous rate of change at \( x = 1 \)** is approximately \( -2 \), which is a reasonable estimate given the steepness of the curve at that point.

Would you like more details on how to calculate the instantaneous rate of change in other contexts or with a different method?

### Related Questions:
1. What is the definition of the derivative and how does it relate to the slope of a curve?
2. How can we calculate the exact slope of a tangent line at a given point using limits?
3. What are some ways to approximate the slope of a curve if the function is unknown?
4. How does the graph's concavity affect the slope of the tangent line?
5. Can we use numerical methods, such as the difference quotient, to find the instantaneous rate of change?

**Tip**: When estimating slopes from a graph, always check if the curve is increasing (positive slope) or decreasing (negative slope).

Estimate the instantaneous rate of change of the function at x = 1 from the graph.

Learn how to estimate the instantaneous rate of change of a function at x = 1 by examining the slope of the tangent line. This problem uses graph analysis to approximate the slope, yielding an estimate of -2. Suitable for students in Grades 10-12 studying calculus concepts.

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