Question

What is the rate of change between the interval of x = 3 pi over 2 and x = 2π?

Answer 1

@TheSmartOne

Answer 2

@zepdrix

Answer 3

@Sila1453

Answer 4

@kittiwitti1

Answer 5

Rate of change is basically a glorified way to say "slope"

lol

Answer 6

yes i know but i don't know how i would put it in terms of the answer choices if that makes sense

Answer 7

like with the unit circle graph

Answer 8

I'd suggest you look up the formula for "average rate of change of a function f(x) on a given interval [a,b]"

Which function are you discussing? Three functions are illustrated. Is it possible that the first function, given as a table of (x,y) values, has the same graph as the 2nd function?

Answer 9

i understand the rate of change just in terms of the answers they give i don't understand how to write it like that look at the answer choices

Answer 10

@mathmale

Answer 11

Given a function f(x) defined on a closed interval [a,b], the average rate of change of this function f(x) on this interval is ... what?

?
average rate of change = -----------------------------
?

Answer 12

You'll need to know this formula for quizzes and exams, so you may as well learn it now.

Answer 13

y^2-y^1/x^2-x^1 i know this are you reading my question

Answer 14

Unfortunately, this is not correct. y^2 represents "the square of y" and is not called for here.

Mind trying again? I'd suggest you actually look up the "average rate of change" formula.

Answer 15

Given a function f(x) defined on a closed interval [a,b], the average rate of change of this function f(x) on this interval is ... what?

?
average rate of change = -----------------------------
?

Answer 16

i didn't mean squared i meant like the second value of y and the 2nd value of x

Answer 17

wait no

Answer 18

a(x)=f(b)-f(a)/b-a

Answer 19

What you have typed definitely means "squared." If you now realize that this is incorrect in this context, then would you please look up the formula for average rate of change?

Answer 20

You are using "a(x)" to denote "average rate of change." But there's no "x" on the right side of your equation.

Instead, write

"average rate of change of f on [a,b]" as the label for your definition.

average rate of change of f on [a,b] = \[\frac{ f(b)-f(a) }{ b-a }\]

Answer 21

THAT is the formula I was asking you to provide.

Answer 22

okay

Answer 23

sorry

Answer 24

Now, what is the function you're working with? In other words, what is f(x)?

Answer 25

well there are three look at the attachment, this is the question Which function has the greatest rate of change on the interval from x = π to x = 3 pi over 2?

Answer 26

OK, right. Then a=pi and b=3pi/2.

For the first function, what is the value of f(a)? of f(b)?

Answer 27

but its in a table i don't understand how to do that

Answer 28

did you look at the attachment?

Answer 29

Don't worry, I have looked at your attachment several times already.

Does x take on the value pi in this table? Does x take on the value 3pi/2 in this table?
If so, read off the corresponding function value, f(a) or f(b), from the table.

Answer 30

I'm sorry i don't get it omg this is frustrating for me lol

Answer 31

f(3pi/2)-f(pi)/3pi/2-pi

Answer 32

Notice that you're not given 3 different graphs; you're given only one graph. Your task is to learn how to read x and y values from various different formats:

from a table
from a graph
from a function

Look at the table; find the first x value, which is a=pi. What is the corresponding y value?

Answer 33

0

Answer 34

Right. So, f(a)=f(pi)=0.
Now find f(b) from the table. b=3pi/2.

Answer 35

-4
so the first two have the same

Answer 36

Unclear what you meant. Clarify that statement, please.

Answer 37

the first two functions have the same rate of change, correct?

Answer 38

Yes. But you have not yet found that average rate of change. Could you do that now?

Answer 39

how though like you plug in the y value?

Answer 40

You don't need to. You are given a table of values.
You have already found out that f(b)=-4 and f(a)=0.

Please evaluate f(b)-f(a).

Answer 41

-4

Answer 42

Right. Now please evaluate b-a.

Answer 43

isn't that still -4

Answer 44

No. Please don't confuse a with f(a), nor b with f(b).

Answer 45

You correctly calculated f(b)-f(a). Use the same skill to calculate b-a.

Answer 46

Remember that a and b are x values, whereas f(b) and f(a) are function values.

Answer 47

What is a?
What is b?
What is b-a?

Answer 48

pi/2

Answer 49

sorry math is really hard for me i promise I'm not dumb lol

Answer 50

correct. Now, what is the average rate of change of the given function over the interval [pi, 3pi/2]?

Answer 51

You have the correct "average rate of change" formula above, remember.

Answer 52

so -4/pi/2?

Answer 53

-8/pi

Answer 54

I see what you are saying, but it'd be better if you presented it as -4/(pi/2).

The latter result can be simplified to -8/pi, yes. very good.

Answer 55

so would that be the rate of change?

Answer 56

AVERAGE rate of change, not just rate of change.

Answer 57

okay

Answer 58

so then what about the last function?

Answer 59

so now you have the ave. r. of c. for the first function.

What is the ave. r. of c. for the 2nd function? Hint: compare table and graph.

Answer 60

same thing

Answer 61

-8/pi

Answer 62

correct. Take a look at the 3rd function. What do you believe is the ave. r. of c. in this case?

Answer 63

Hint: What is the value of [4(0)+2] - [4(-4)+2]?

Answer 64

16

Answer 65

Yes, and what is the ave. r. of c. of the 3rd function on the given interval?

Answer 66

32/pi?

Answer 67

Yes. very good. Any questions?

Answer 68

so h(x) has the greatest avg r of c?

Answer 69

yes. the first 2 are equal to 8/pi and the third is equal to 16/pi.

Answer 70

can u help with one more?

Answer 71

Or did we lose a negative sign in there somewhere? Double check your work.

What's the next problem all about?

Answer 72

im so confused is that not right

Answer 73

its a similar problem i just wanna make sure I'm getting it

Answer 74

Too early for you to say "I'm so confused." What average rate of change did you obtain earlier for the first 2 functions?

Answer 75

-4/pi

Answer 76

-8/pi oops

Answer 77

ok so h(x) would still have the greatest

Answer 78

So, now, you are comparing -8/pi to the ave. r. of c. of the 3rd function. Yes, h(x) has the greatest ave. r. of c. of the 3 given functions. on the given interval.

Answer 79

ok, can u pls help me with another

Answer 80

There's no short cut; you have to calculate the actual ave. rates of change and then compare them at the end.

Answer 81

Let's see the new problem.

Answer 82

so for the numerator would it be 2?

Answer 83

and then the denominator pi?

Answer 84

so 2/pi

Answer 85

First: what are the y-values corresponding to the given x values?

What is b-a?

What is f(b)-f(a)?

Answer 86

3-1 for b-a?

Answer 87

-pi/2 for denominator

Answer 88

How'd you get that? a and b are x-values. I don't see "1" or "3" on the x-axis of the graph.

Answer 89

I'm sorry i got them mixed up, 3-1 would be the f values

Answer 90

a=?
b=?

Answer 91

a=2pi b=3pi/2

Answer 92

or would it be the other way

Answer 93

You tell me.