# Average Rate of Change

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

1. ### 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.

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
2. ### MathLover1

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yes =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.

MathLover1, May 18, 2022
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3. ### 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
4. ### 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

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Is this the calculus way?

nycmathguy, May 19, 2022
6. ### MathLover1

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it's simple algebra way

MathLover1, May 19, 2022
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7. ### 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
8. ### MathLover1

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previous way I did is the calculus way

MathLover1, May 19, 2022
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9. ### MathLover1

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GRE, why you need that?

MathLover1, May 19, 2022
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