Estimate Instantaneous rate of change
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1. Describe the blue line. What makes it a secant line?
2. What is the average rate of change from A to B on the interval from [1, 4]?
3. What is the average rate of change from A to B when B is moved to x = 3?
4. What is the average rate of change from A to B when B is moved to x = 2?
5. What is the average rate of change from A to B when B is moved to x = 1.5?
6. What is the average rate of change from A to B when B is moved to x =1.1?
7. What is the average rate of change from A to B when B is moved to x = 1.01?
8. As point B moves toward point A, describe 3 things that happen.
9. Describe the green line. What makes it a tangent line?
10. Approximate the instantaneous rate of change at x = 1 when the interval between A and B is zero by calculating the slope of the green tangent line.
11. How does your answer to number 10 compare to your values for your average rates of change as B moved closer to A?