Water coming out of a fountain is modeled by the function f(x) = −x2 + 6x + 6 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 = 2 to x = 5 represent?

Question

Water coming out of a fountain is modeled by the function f(x) = −x2 + 6x + 6 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 = 2 to x = 5 represent?

Imagine · Answer

Good Morning, Angel. Do you have any choices to choose from? If so, please post them below.

Imagine · Answer

I'll start with writing the formula, while you look for your choices;
$$\frac{ F(a)-f(a) }{ b-a}$$
Now, could we get those choices, please?

RaeRae · Answer

Morning! What did you get first Angel?

snowflake0531 · Answer

I helped you with this already, scroll down https://questioncove.com/users/angelcook2007#/updates/60ac230355854fb88b1bf000 just find the slope between (2,14) and (5,11)

snowflake0531 · Answer

$$\frac{ y_{2}-y_{1} }{ x_{2}-x_{1} }$$ $$(2,14)=>(x_{1},y_{1})\(5,11)=>(x_{2}-y_{2})$$

angelcook2007 · Answer

oh, hello, sorry I wasn't paying attention

angelcook2007 · Answer

@imagine wrote:

I'll start with writing the formula, while you look for your choices; $$\frac{ F(a)-f(a) }{ b-a}$$ Now, could we get those choices, please?

The water travels an average distance of 4 feet from 2 seconds to 5 seconds. The water travels an average distance of 1 foot from 2 seconds to 5 seconds. The water falls down with an average speed of 2 feet per second from 2 seconds to 5 seconds. The water falls down with an average speed of 1 foot per second from 2 seconds to 5 seconds.

angelcook2007 · Answer

@snowflake0531 wrote:

I helped you with this already, scroll down https://questioncove.com/users/angelcook2007#/updates/60ac230355854fb88b1bf000 just find the slope between (2,14) and (5,11)

-1?

snowflake0531 · Answer

Yes!
the slope is -1, which means every second, it falls 1 feet
so what's the answer?

angelcook2007 · Answer

um

angelcook2007 · Answer

either b or d?

angelcook2007 · Answer

wait no

angelcook2007 · Answer

It's D

angelcook2007 · Answer

@snowflake0531

snowflake0531 · Answer

@angelcook2007 wrote:

It's D

yeah it's D

angelcook2007 · Answer

Okay, thank you

snowflake0531 · Answer

yw~