## anonymous one year ago FAN AND MEDAL! What is an approximate average rate of change of the graph from x = 3 to x = 5 for f(x)=-13.333(x - 3)^2+120 ?

1. anonymous

@ganeshie8 @geny55 @LifeIsADangerousGame @KAKES1967 @JoannaBlackwelder @Michele_Laino @Nnesha @Bookworm14 @vera_ewing @cj49 @Xaze @zepdrix @JoannaBlackwelder @Hero @ganeshie8 @fratdog123 @DullJackel09 @sourwing @abb0t @Shalante

2. anonymous

$\frac{ f(5)-f(3) }{ 5-3 }$

3. anonymous

f(x)=-13.333(x - 3)^2+120 is the equation f(5)=-13.333(x - 5)^2+120 f(5)=-13.333x^2-333.33 @Shalante is this right so far?

4. anonymous

Nope, no need to change the (x-3)

5. anonymous

f(x)=-13.333(x - 5)^2+120 is the equation f(5)=-13.333(x - 5)^2+120 f(5)=-13.333x^2-333.33+120 f(5)=-13.333x^2-213.33

6. anonymous

Do not change anything besides the x Plug in x=5 and x=3 Subtract f(5)-f(3) Divide it by 2 since that is the interval difference.

7. anonymous

so how would i solve it? i need to show the steps

8. anonymous

f(x)=-13.333(5 - 3)^2+120 is the equation f(5)=-13.333(2)^2+120 f(5)=-13.333(4)+120 ?

9. anonymous

f(5)=-13.333(4)+120 f(5)=-53.33+120 f(5)=66.67 ??

10. anonymous

replace x with 5 to get answer #1 replace x with 3 to get answer #2 (answer #1 - answer #2) / 2

11. anonymous

@Shalante did i solve it for x=5 correctly tho?

12. anonymous

yea f(5) is correct.

13. anonymous

ok and then f(x)=-13.333(x - 3)^2+120 f(3)=-13.333(3 - 3)^2+120 f(3)=-13.333(0)+120 f(3)=120 ?

14. anonymous

Yes. now subtract it and then divide by 2

15. anonymous

66.67-120/2 -53.33/2 -26.67

16. anonymous

is that right?

17. anonymous

Yes, that is correct.

18. anonymous

ok thanks!

19. anonymous

what does this rate represent in this situation? The graph below shows a company's profit f(x), in dollars, depending on the price of pens x, in dollars, being sold by the company:

20. anonymous

-26.67 means the slope is decreasing at an average of 26.67 from x=3 to x=5

21. anonymous

the rate of the profit they are getting. rate is change of y. y is f(x) f(x) is the profit.

22. anonymous

so their profit is decreasing by 66.67?

23. anonymous

You mean decreasing by 26.67?

24. anonymous

oh yea lol

25. anonymous

Yes, from 3 shirts sold to 5 shirts, the profit decreased by an average of \$26.67.

26. anonymous

ok thanks gtg!!

27. anonymous

No problem!