## anonymous one year ago Water coming out from a fountain is modeled by the function f(x) = -x2 + 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? 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

1. freckles

average rate of change is given by the change of y over the change of x. $\frac{ f(5)-f(3)}{5-3}$

2. freckles

you are dividing a change of height by a change in time

3. anonymous

So x = 2?

4. dumbcow

also "rate of change" = speed

5. anonymous

So, I know its either A or B, right?

6. dumbcow

yes

7. anonymous

So its either 5 or 3 feet per 3-5 seconds?

8. freckles

just used the formula I gave above to figure out between A and B

9. anonymous

I dont understand the formula you gave me.

10. anonymous

f(5) - f(3) = f(2) ----- 2 ??????????????

11. freckles

...how did you get f(5)-f(3)=f(2)?

12. freckles

f(5)=-5^2+5(5)+4 and f(3)=-3^2+5(3)+4

13. anonymous

So f(5) = 3154 And f(3) = 110

14. freckles

-5^2+5(5)+4 ------ first we know 5^2=5(5)=25 so -5^2+5(5)+4 can be written as -25+25+4

15. freckles

-25+25 is 0 though so you have -5^2+5(5)+4 can be written as 0+4 which is just 4

16. freckles

can you try doing f(3)

17. anonymous

f(3) = 25?

18. freckles

are you guessing?

19. anonymous

No

20. freckles

f(x)=-x^2+5x+4 just plug in 3 where x is

21. anonymous

OH there is a negative, my bad

22. freckles

f(3)=-3^2+5(3)+4 3^2 means 3(3) which is 9 5(3) is 15 f(3)=-9+15+4

23. anonymous

so 10?

24. freckles

$\frac{f(5)-f(3)}{5-3}=\frac{4-10}{5-3}$

25. anonymous

so its 3

26. anonymous

27. freckles

well -3 where the units is distance/time which is a speed unit which just means going down at a speed of 3ft/sec

28. freckles

and yes a sounds great

29. anonymous

Thx for the help! Ima submit my test now, lets see :D

30. anonymous

Oh no! I got a %62 on my test :(. 5 questions wrong out of 13. But the one you helped me with was right, ty so much!