Average Rate Of Change And EquationsPresentation Transcript
Average Rate of Change and Equations…
Do Now: The height, in feet, of a ball thrown into the air is modeled by h(t) = - 16t 2 – 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 y -axis use 5 boxes = 40 feet.
How far did the ball travel from t = 0 to t = 2 seconds?
What was the average distance traveled for the first two seconds?
64 ft per second
What is another name for this?
Draw a line connecting (0, h (0)) and (2, h (2)). What is this line?
What does the average distance traveled (per second) represent in terms of this line?
Write the equation of this line.
y – 0 = 64(x – 0) or y – 128 = 64(x – 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
The secant line
In general, as the interval get smaller (as b gets closer to a ), what line are we approximating?
In terms of the original problem, what does this represent?