Average Rate of Change

Discussion in 'Algebra' started by nycmathguy, May 18, 2022.

  1. nycmathguy

    nycmathguy

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    Math 004 sample test questions for anyone seeking NYS certification as a high school math teacher. This is just one of several exams required for NYS high school teacher certification.

    Screenshot_20220517-215129_Samsung Internet.jpg

    Let A = average rate of change.
    Let me know if the set up is correct.

    A = [-16(3)^2 + 64(3) + 5 - (-16(1]^2 + 64(1) + 5]/(3 -1)

    Yes?
     
    nycmathguy, May 18, 2022
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  2. nycmathguy

    MathLover1

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    yes upload_2022-5-17_22-30-14.gif =0

    explanation:

    The height of the ball is a function of time, so the equation can be expressed as

    f(t) = -16t^2 + 64t + 5, and the average rate of change can be found by calculating

    (f(3) − f(1))/(3 − 1) .

    (-16(3)^2 + 64(3) + 5 - (-16(1)^2 + 64(1) + 5))/2 = (53 - (53))/2 = 0/2 = 0

    Alternatively, the rate of change can be determined by finding the slope of the secant line through
    points (1,f(1)) and (3,f(3)).

    Notice that this is a horizontal line, which has a slope of 0.
    upload_2022-5-17_22-30-56.png
     
    MathLover1, May 18, 2022
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  3. nycmathguy

    nycmathguy

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    You said:

    "Alternatively, the rate of change can be determined by finding the slope of the secant line through
    points (1,f(1)) and (3,f(3))."

    By "slope of the secant line" you mean the derivative of the secant line. Yes? If so, can you show me how to do this the calculus way?
     
    nycmathguy, May 18, 2022
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  4. nycmathguy

    MathLover1

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    f(t) = -16t^2 + 64t + 5

    f(1) = -16*1^2 + 64*1 + 5=53
    f(3) = -16*3^2 + 64*3+ 5=53
    points
    (1,f(1)) =(1,53)
    (3,f(3))=(1,53)

    slope=(53-53)/(1-1)=0
     
    MathLover1, May 18, 2022
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  5. nycmathguy

    nycmathguy

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    Is this the calculus way?
     
    nycmathguy, May 19, 2022
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  6. nycmathguy

    MathLover1

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    it's simple algebra way :)
     
    MathLover1, May 19, 2022
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  7. nycmathguy

    nycmathguy

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    The algebra way is easier but would love to see the calculus way. Later tonight, I will post 5 GRE math applications. GRE stands for GRADUATE RECORD EXAMINATION. This test is for students wishing to enter certain graduate schools.
     
    nycmathguy, May 19, 2022
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  8. nycmathguy

    MathLover1

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    previous way I did is the calculus way
     
    MathLover1, May 19, 2022
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  9. nycmathguy

    MathLover1

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    GRE, why you need that?
     
    MathLover1, May 19, 2022
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  10. nycmathguy

    nycmathguy

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    I don't need the GRE but I do need practice with math word problems. I am not taking state exams for jobs at 57 years old. However, study books have lots of great practice word problems. You say?
     
    nycmathguy, May 19, 2022
    #10
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