## anonymous 4 years ago Find the average rate of change of the function y = x^2 - 3x + 5 over the interval [-1,3]

1. amistre64

$\frac{f(3)-f(-1)}{3--1}$

2. amistre64

hopefully, you know what f(3) and f(-1) mean :)

3. amistre64

f(3) = 3^2 - 3(3) + 5 = 5 f(-1) = (-1)^2 -3(-1) + 5 = 10

4. amistre64

5 - 10 ----- = avg rate of change 4

5. amistre64

3+1 = 4 + 5 = 9 , not 10

6. amistre64

sooo close lol

7. amistre64

5-9 ---- = -1 then :) 4

8. anonymous

yes, thank you it is the derivative of b minus deriv of a, all over function b - function a

9. anonymous

right...

10. amistre64

derivatives are instantaneous rates of change; average rates are just last - first divided by well, b-a

11. amistre64

i wonder if derivs work out as well 2x-3; 2-3 = -1 , 6-3 = 3 -1-3 ---- = -1 hmmm, might be on to something there 3+1

12. myininaya

you are just looking for the slope of the secant line that lies on the curve y=x^2-3x+5 touching the two points (-1,f(-1)) and (3,f(3))

13. amistre64

nope, 2(-1)-3 = -5

14. myininaya

so basically you learn how to find average rate of change in algebra

15. myininaya

its just the slope of a line

16. amistre64

farm says I shouldnt harass you for your banning techniques :)

17. myininaya

shhh i will accidentlly ban you

18. amistre64

:) practice makes perfect

19. anonymous

wait, i am confused a little bit, what do i do in simple steps to solve this?

20. amistre64

(3^2-3(3)+5) - ((-1)^2-3(-1)+5) ----------------------------- 3-(-1)

21. amistre64

|dw:1327862346587:dw|

22. anonymous

that is equal to -1 right

23. amistre64

the avg rate of change is just the slope of the line between 2 points

24. amistre64

the instant rate of change is the slope of the tangent line to the curve at a point; also known as the derivative

25. anonymous

okay, i'm good

26. amistre64

yay!! :)