Question

If f(x)=3x−6x−2, what is the average rate of change of f(x) over the interval [6, 8]?

Answer 1

A. 0
B. 1
C. 3
D. 3.5

Answer 2

those are the options, will give medals! please help!!! @abb0t @AngelWilliams16 @bradenhart @Gokuporter @Taylor<3sRin

Answer 3

Average rate of change is the secant line from connecting those two points

Answer 4

how do you find that?

Answer 5

find f(6) and f(8) first

Answer 6

Slope of secant line

Answer 7

just saw that .. yeah *Slope

Answer 8

i'm AWFUL at math....so how would you solve for f?

Answer 9

\[\frac{ f(6) - f(8) }{ 6 - 8 }\]

Answer 10

Let X = 6 and calculate f(6 =

Answer 11

Solve for \(f\)? They already gave \(f\) to you.

Answer 12

f(6) = 3*6 - 6*6 - 2

Answer 13

theres the question...i'm very confused:/

Answer 14

\[ave change = \frac{ f(6) - f(2) }{ 6-2 } = \frac{ -20 - (-8) }{ 6 - 2 }\]

Answer 15

Average rate of change of a function over the interval\[x _{1} \le x \le x _{2}\]is given by\[\frac{ f(x _{2})-f(x _{1}) }{ x _{2}-x _{1} }\]

Answer 16

It is just the slope of the line connecting the points at the endpoints of the interval. as above

Answer 17

@DanJS you're not supposed to give out the answers. You're supposed to teach.

Answer 18

so 3x-6/x-2....but they already gave that to me...

Answer 19

Which question do youw ant to do, the one you posted first , or the linked one?

Answer 20

it's the same question...

Answer 21

did i mistype something?

Answer 22

no, you typed it differently. ill go with the link

Answer 23

that's the correct one:)

Answer 24

so
\[f(x) = \frac{ 3x - 6 }{ x - 2 }\]
Evaluate that at x = 6 and at x = 8

Answer 25

for example f(6) = (3*6 - 6) / (6-2) = 12 / 4 = 3

Answer 26

now do f(8)

Answer 27

i got what you just did @DanJS

Answer 28

right , so find out what f(8) is now

Answer 29

Then use this

\[slope = \frac{ f(6) - f(8) }{ 6 - 8 }\]

Answer 30

Slope is the average rate of change over that interval [6,8]

Answer 31

ok, \(f(x) = 3x−6x−2\)

you want to find the average RoC, and that is found by \(\dfrac{f(b) - f(a)}{b-a}\)

First find \(f(8)~,~ f(8) = 3(8)-6(8)-2\).

Then find \(f(6) ~,~ f(6)= 3(6)-6(8)-2\)

Then just plug it into your formula.

Answer 32

@DanJS , you're solving it like \(\dfrac{f(a)-f(b)}{a-b}\), seems a little opposite.

Answer 33

it doesnt matter

Answer 34

Oh, hm, thought it would make a difference in the slope.

Answer 35

nah

Answer 36

neg/neg = pos/pos, either way you look at it

Answer 37

So where you at with it SPECEK

Answer 38

sorry trying to keep up with everyone!:) so 3 would be the average rate of change?

Answer 39

not sure, i didnt calculate it, what did you do

Answer 40

im going to post a pic. one sec:)

Answer 41

ok, ill type the result in the mean time

Answer 42

that's all i've got..

Answer 43

\[f(8) = 0\]
f(6) = 0

\[\frac{ f(8) - f(6) }{ 8 - 6 } = \frac{ 3 - 3 }{ 2 } = \frac{ 0 }{ 2 } = 0\]

Answer 44

It is a horizontal line actually, the rate of change is zero

Answer 45

f(8) = 3
f(6) = 3

Answer 46

huh....i do understand how you did that:) thank you so much! could you help me with a few more problems?

Answer 47

i put zero in the one above on accident for f(8) and f(3) they are both 3

Answer 48

Here look at this, it can help you

Answer 49

wait so the rate of change is 3 or 0???

Answer 50

\[f(x) = \frac{ 3x - 6 }{ x - 2 } = \frac{ 3(x-2) }{ (x-2) } = 3\]

Answer 51

It is a horizontal line at y = 3 ...f(x) = 3

Answer 52

okay so 3? want to make sure!!

Answer 53

no the rate of change of a horizontal line, is zero

Answer 54

alright. sorry all of this confuses me! i'm going with 0!

Answer 55

the y coordinate does not change as the x coordinate changes in a horizontal line, the slope is zero

Answer 56

here to summarize...

Answer 57

f(x) = (3x-6)/(x-2)

Average rate of change btween two points is the slope.
\[slope = \frac{ change of y }{ change of x } = \frac{ f(8) - f(6) }{ 6-8 } = \frac{ 3 - 3 }{ 2 } = \frac{ 0 }{ 2} = 0\]

The average rate of change of f(x) over the interval [6,8] is ZERO.

Answer 58

That is it

Answer 59

okay:) thank you!!

Answer 60

heres my next question...

Answer 61

@DanJS

Answer 62

This would be the same thing...

\[ave change = \frac{ f(3) - f(-2) }{ 3 - (-2) }\]

Answer 63

They gave you a table of values, so you dont have to calculate f(3) and f(-2)

Answer 64

i have trouble setting it up. lemme confirm the answer with you?:)

Answer 65

type out the first step

Answer 66

plugging in the values?

Answer 67

the interval is [-2 , 3]
find f(-2) and f(3) from the table

Answer 68

i got 2.5/5

Answer 69

which equals half, .5

Answer 70

correct?

Answer 71

no

Answer 72

watch..

Answer 73

The interval is over x=-2 to x=3 , [-2, 3]
from table
f(-2) = 2.5
f(3) = 5

average Rate of Change over [-2,3] =
\[\frac{ f(3) - f(-2) }{ 3 - (-2) } = \frac{ 5 - 2.5 }{ 3 + 2 }\]

Answer 74

oh i see, you just gave me the final answer... yeah it is 2.5/5

Answer 75

I thought you just divided the f(-2) and f(3)

Answer 76

yeah i'm sorry! i have trouble explaining myself.

Answer 77

but the final would be half?

Answer 78

So all you need to remember for the AVERAGE RATE OF CHANGE

y = f(x); over an interval [a,b]

Ave change =
\[\frac{ f(b) - f(a) }{ b - a }\]

average change is found by evaluating the function f(x) at x=b and x=a, then using the above formula.

Answer 79

yeah final 2.5/5 = 1/2

Answer 80

okay...thank you so much for your patience with me. it means SOO much! @DanJS i just have two more questions...

Answer 81

of course! thank you lots