• Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Be the first to comment
    Be the first to like this
No Downloads

Views

Total Views
56,367
On Slideshare
0
From Embeds
0
Number of Embeds
6

Actions

Shares
Downloads
19
Comments
0
Likes
0

Embeds 0

No embeds

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
    No notes for slide

Transcript

  • 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
  • 5.
    • 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?