Average Rate Of Change And Equations

Text-only Preview

  1. Average Rate of Change and Equations…
  2. 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?
    • 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 – 0 = 64(x – 0) or y – 128 = 64(x – 2)
  3. 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
  4. 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?
    • tangent line
    • In terms of the original problem, what does this represent?
    • Instantaneous velocity
    • In general, how can we represent this?