Average Rate Of Change And Equations

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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. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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: ,[object Object],[object Object],The secant line

[object Object],[object Object],[object Object],[object Object],[object Object]

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15.) Line L in the figure below is parallel to the line y=4x+2. Find the coordinates of the point P P= 19.) Match the Lines L1 (blue), L2 (red) and L3 (green) with the slopes by placing the letter of the slopes next to each set listed below The slope of line L2: The slope of line L3: The slope of line L1: A. m=−1. B. m=0 C. m=0.2 24.) The height s of a ball (in feet) at time t(in seconds) is given by the formula s(t)=64−16(t−1) s(t)=64−16(t−1)^2 . Consider the following expression. AV[0.5,1]=s(1)−s(0.5)/1−0.5 Compute the value of AV[0.5,1]= What does this value measure geometrically? slope. The slope of the line between the points (0.5,s(0.5))and (1,s(1))(1,s(1)). curvature. The curvature of the graph of ss on the interval 0.5≤t≤1. area. The area under the graph of ss on the interval 0.5≤t≤1. distance. The distance between the points (0.5,s(0.5)) and (1,s(1))(1,s(1)). What does this value measure physically? average velocity. The average velocity of the ball during the interval 0.5≤t≤10.5≤t≤1. distance. The distance that the ball travels during the interval 0.5≤t≤10.5≤t≤1. direction. The direction that the ball traveling during the interval 0.5≤t≤10.5≤t≤1. acceleration. The acceleration of the ball during the interval 0.5≤t≤10.5≤t≤1. What are the units on AV[0.5,1]AV[0.5,1]? feet per second feet seconds feet per second squared foot seconds none of these 15.) Line L in the figure below is parallel to the line y=4x+2. Find the coordinates of the point P P= 19.) Match the Lines L1 (blue), L2 (red) and L3 (green) with the slopes by placing the letter of the slopes next to each set listed below The slope of line L2: The slope of line L3: The slope of line L1: A. m=−1. B. m=0 C. m=0.2 24.) The height s of a ball (in feet) at time t(in seconds) is given by the formula s(t)=64−16(t−1) s(t)=64−16(t−1)^2 . Consider the following expression. AV[0.5,1]=s(1)−s(0.5)/1−0.5 Compute the value of AV[0.5,1]= What does this value measure geometrically? slope. The slope of the line between the points (0.5,s(0.5))and (1,s(1))(1,s(1)). curvature. The curvature of the graph of ss on the interval 0.5≤t≤1. area. The area under the graph of ss on the interval 0.5≤t≤1. distance. The distance between the points (0.5,s(0.5)) and (1,s(1))(1,s(1)). What does this value measure physically? average velocity. The average velocity of the ball during the interval 0.5≤t≤10.5≤t≤1. distance. The distance that the ball travels during the interval 0.5≤t≤10.5≤t≤1. direction. The direction that the ball traveling during the interval 0.5≤t≤10.5≤t≤1. acceleration. The acceleration of the ball during the interval 0.5≤t≤10.5≤t≤1. What are the units on AV[0.5,1]AV[0.5,1]? feet per second feet seconds feet per second squared foot seconds none of these 1.) Find the slope and the equation for the line passing through the point (−6,8)(−6,8) with yy-intercept at y=−1y=−1. a) m= b) The equation for the line in slope-intercept form: 2..

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1. Average Rate of Change and Equations…

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.

5.