Question

Water coming out from a fountain is modeled by the function f(x) = -x^2 + 5x + 4 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 of f(x) from x = 3 to x = 5 represent?

Answer 1

The water falls down with an average speed of 3 feet per second from 3 seconds to 5 seconds.
The water falls down with an average speed of 5 feet per second from 3 seconds to 5 seconds.
The water travels an average distance of 3 feet from 3 seconds to 5 seconds.
The water travels an average distance of 5 feet from 3 seconds to 5 seconds.

Answer 2

HI!!

Answer 3

it is the average speed you are computing

Answer 4

Averate rate of change has the formula kinda like the slope ;)
\[ \text{ Average Rate of Change }=\frac{f(5)-f(3)}{5-3}\]

Answer 5

to find it you need to compute the numbers

Answer 6

what @Mimi_x3 wrote

Answer 7

ooh no dear

Answer 8

\[f(5)-f(3)\neq f(2)\] you gotta compute!

Answer 9

Umm slight mistake there
f(5)= -(5)^2 + 5(5) + 4
f(3) = -(3)^2 + 5(3) + 4
You need to plug these in

Answer 10

no shortcuts just compute
\[f(5)\] then compute \[f(3)\] then subtract

Answer 11

\[ f(x) = -x^2 + 5x + 4\\
f(5) = -5^2 + 5\times 5 + 4\]

Answer 12

\[f(x) = -x^2 + 5x + 4\\
f(3) = -3^2 + 5\times 3 + 4\]

Answer 13

\[\text{ Average Rate of Change }=\frac{f(5)-f(3)}{5-3}\]
\[\text{ Average Rate of Change }=\frac{(-5^2 + 5( 5) + 4)-(-4^2 + 5(4) + 4)}{5-3}\]

Answer 14

f(5) = 4
f(3) = 10

4-10 = -6

So... \[\frac{ -6 }{ 2 }\] ???

Answer 15

ayee whoops I did 4 instead of 3 in my post above -.-
Anyways so you are right ...
what -6/2???

Answer 16

I have no clue what I'm doing. o.o

Answer 17

hmmm want me to explain????

Answer 18

well anyways what -6/2