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Average Rate of Change and Equationsâ€¦ Do Now: The height, in feet, of a ball thrown into the air is modeled by h(t) = - 16t 2 â€“ 96t ,…

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- Average Rate of Change and Equationsâ€¦
- Do Now: The height, in feet, of a ball thrown into the air is modeled by h(t) = - 16t 2 â€“ 96t , where t is measured in seconds. Graph the height of the ball seconds on the following grid. Use a scale on the x -axis of 3 boxes = 1 second. On the yÂ -axis use 5 boxes = 40 feet.
- How far did the ball travel from t = 0 to t = 2 seconds?

- 128 Ft

- What was the average distance traveled for the first two seconds?

- 64 ft per second

- What is another name for this?

- average velocity

- Draw a line connecting (0, h (0)) and (2, h (2)). What is this line?

- secant line

- What does the average distance traveled (per second) represent in terms of this line?

- slope

- Write the equation of this line.

- y â€“ 0 = 64(x â€“ 0) or y â€“ 128 = 64(x â€“ 2)

- In general, __________________________________, can be found by using the formula: The average rate of change of a function (slope of the secant) Where [a,b] is a closed interval on which f is defined
- The equation of ___________________________, can be found by:
- 1. Finding the slope of the secant (AROC)

- 2. using point/slope with either point

- In general, as the interval get smaller (as b gets closer to a ), what line are we approximating?

- tangent line

- In terms of the original problem, what does this represent?

- Instantaneous velocity

- In general, how can we represent this?

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