Average Rate of Change

[nycmathguy]

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?

 

[MathLover1]

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.

 

[nycmathguy]

yes View attachment 3100=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.
View attachment 3101

yes View attachment 3100=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.
View attachment 3101

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?

 

[MathLover1]

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

 

[nycmathguy]

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

Is this the calculus way?

 

[MathLover1]

Is this the calculus way?

it's simple algebra way

 

[nycmathguy]

it's simple algebra way

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.

 

[MathLover1]

previous way I did is the calculus way

 

[MathLover1]

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.

GRE, why you need that?

 

[nycmathguy]

GRE, why you need that?

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?