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Math Help - Average/Instantaneous rate of change questions.

  1. #1
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    Average/Instantaneous rate of change questions.

    1. Which function has a negative average rate of change on the interval 1<x<4?

    a) f(x) = x^2 - x - 1
    b) g(x) = 1.6x - 2
    c) h(x) = -x^2 + 9
    d j(x) = -3

    2. For which value of x is the instantaneous rate of change of h(x) = 0.5x^2 + x - 2 closest to 0?

    a) x= -1
    b) x= -1
    c) x= 0
    d x= 1

    3. Martin walks 5 m toward a motion sensor over the course of 10 s, at a constant speed. What would be the slope of the segment representing this walk on a distance versus time graph?

    a) -2
    b) -1/2
    c) 1/2
    d) 2

    4. A student is walking in a straight line infront of a motion sensor. The sensor begins collecting data when the student is 6 m away. The student walks toward the sensor for 4 s at a rate of 1m/s. Then she walks away from the sensor for 8 s at a rate of 0.5 m/s. Which of the points is on the graph of the distance versus time?

    a) (6, 0)
    b) (8,2)
    c) (10, 6)
    d) (12,6)

    5. Myra is riding a Ferris Wheel. Her height h(t), in metres above the ground at time t seconds, can be modelled by h(t) = 10sin(6(t-20)) + 10. At what time will Myra's car be at its greatest height?

    a) t=20s
    b) t=35s
    c) t=40s
    d) t=55s

    6. At which point on the graph of f(x) = -x^2 -2x + 15 is the slope of the tangent 0?

    a. (-2,15)
    b. (-1, 16)
    c. (0, 15)
    d. (3,0)

    -------------------------
    For the image below, (number 5 and 6)

    for the first graph where it says, Which graph models walking directly away from a motion sensor at a constant rate?

    It is letter C?

    For number 6, is it D, cannot be determined because its staying still? Or could it be intervals 5<t<7 (b)?
    Attached Thumbnails Attached Thumbnails Average/Instantaneous rate of change questions.-mh4u1-2-.jpg  
    Last edited by mr fantastic; December 4th 2011 at 09:57 AM. Reason: Title.
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  2. #2
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    Re: Average/Instantaneous rate of change(verify my answers please)

    Most are correct although I believe that #4 has two correct answers (initially, t= 0 and we are told she was 6 m from the sensor). 5 is correct assuming that "sin(x)" has x in degrees which is not standard when sine and cosine are used simply "as functions" rather than with angles. For 6, no, it is not "staying still". That is a graph of speed at time t, not position. A horizontal line means moving at that constant speed. And, as long as speed is constant, distance moved is just "speed times time", much like the area of a rectangle is "height time base"- which is why the distance moved is given by the area under the speed graph.
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  3. #3
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    Re: Average/Instantaneous rate of change(verify my answers please)

    For h(t) = 10sin(6(t-20)) + 10, it is 20 degrees, it does not really matter does it?

    For number #4, I know it is between these two answers (10, 6)
    (12,6) since y= 6

    For number 6, the answer has to be a then, interval 0<t<5?


    By the way, is it ok if I post more questions in this thread to verify my answers? T.T

    --------------------------------------------------------------------------------------------------

    In the graph below, it says A distance versus time graph is shown below. What is the instantaneous rate of change in the distance at t = 6s.

    I did like this

    First I found out the equation from 4 to 8 seconds, which gave me y=1/4x + 3.

    Second, to find the instantaneous, I used values closer to 6s, -> 5.99 and 6.01

    Third, I use the equation to calculate

    y=1/4x + 3

    y= 1/4(6.01) + 3
    =4.5025

    y= 1/4(5.99) + 3
    = 4.4975

    then I used Y2-Y1/X2-X1

    =4.5025-4.4975/6.01-5.99
    = 0.25 m/s?

    Therefore, the instantaneous rate of change is 0.25 m/s.
    Attached Thumbnails Attached Thumbnails Average/Instantaneous rate of change questions.-img-20111204-00028.jpg  
    Last edited by Oxidized; December 4th 2011 at 08:35 AM.
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