Question

Water coming out from a fountain is modeled by the function f(x)=-x^2+8x+2 where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds.

What does the average rate of change f(x) from x=1 to x=4 represent?

The water travels an average distance of 3 feet from 1 second to 4 seconds.
The water travels an average distance of 2 feet from 1 second to 4 seconds.
The water rises up with an average speed of 3 feet per second from 1 second to 4 seconds.
The water rises up with an average speed of 2 feet per second from 1 second to 4 seconds.

Answer 1

Please explain how instead of just saying the answer, thanks!

Answer 2

@SamsungFanBoy

Answer 3

@Dolkun

Answer 4

@MikeyMaximum

Answer 5

@mrbaconqwerty

Answer 6

Dont know. Sorry :(

Answer 7

That's fine, thank you for at least checking it out (:

Answer 8

@Chris01 ?

Answer 9

@Tuta

Answer 10

I feel like it's either A or C but I'm not sure how to differentiate (sorry if I spelt that wrong) the two

Answer 11

don't really know how to explain it. but im pretty sure its B

Answer 12

Do you know how you got b? :/

Answer 13

find the values of f at x = 1 and x = 4. Then you'll subtract these values. This will give you the absoulte change.

Then divide the absolute change over the interval by the length of the interval, to find the average amount of change in f(x) per one-unit change in x

Answer 14

I did that, and I got (1,9) and (4,18) I subtracted 18 by 9 and got 9, and 4-1=3. so 9/3=3 and that's why I thought it was A or C

Answer 15

can you help figure this out @Ashleyisakitty

Answer 16

cause i'm still thinking its B

Answer 17

Can you maybe input the numbers and everything so I know how you got B?

Answer 18

ok

Answer 19

Thanks

Answer 20

I'm leaning toward C and D now /:

Answer 21

i'm lagging so bad sorry if i'm taking so long

Answer 22

It's totally fine, since I do online, I could turn this in whenever. Haha.

Answer 23

I just don't want to be wrong because this is on one of my final exams and yeah :|

Answer 24

@mathmate

Answer 25

@corruptedalice96
The first two choices said "the average distance travelled" which implies the curved distance travelled. The question asks for the change in f(x), which relates to the height.
This information together with Chris01's will enable you to get the right answer.

Answer 26

I'm still confused, do you think you could explain, but with different numbers?

Answer 27

I'm pretty confident it's C but I don't know if that's right

Answer 28

@mathmate ?

Answer 29

f(x)=-x^2+8x+2
differentiate f(x) with respect to x:
f'(x)=-2x+8
where f'(x) represents the vertical speed (rate of change) as a function of time.
f'(1)=+6
f'(4)=+0
Average speed (rate of change) = (f'(1)+f'(4))/2 = (6+0)/2 = 3 fps

To find the derivative (i.e. result of differentiation) see
http://www.wikihow.com/Differentiate-Polynomials

Answer 30

I'm so lost..

Answer 31

the drawings should help.
If you would review this term's work on derivatives and functions, it would be much easier to follow.

Answer 32

@mathmate I'm going with C then..

Answer 33

@♪Chibiterasu do you think you could check my answer?

Answer 34

@iGreen

Answer 35

@nincompoop

Answer 36

ITS THE ANSWER C OR D? @CORRUPTEDALICE96