## ChrisV 3 years ago Find the average rate of change of the function over the given interval. Compare the average rate of change with the instant rate of change at the endpoints of the interval. f(x)=-1/x [1,2]

1. ChrisV

f(x)=-1x^-1 -1(-1)x^-2 1/x^2

2. ChrisV

1/(1)^2=1 1/(2)^2=2 instantaneous rates: f'(1)=1 ; f'(2)= 1/4

3. ChrisV

how do i find the average rate?

4. ChrisV

i know the average rate is 1/2 because the back of the book tells me, but I do not see how to get that from my work. :(

5. dumbcow

think of slope between the 2 endpoints avg rate = f(2) -f(1) / 2-1 = -1/2 -(-1) / 1 = 1/2

6. ChrisV

so basically f(1)-f(2)?

7. dumbcow

or more technically using calculus $avg rate = \frac{1}{b-a}\int\limits_{a}^{b}f'(x) dx = \frac{f(b) -f(a)}{b-a}$

8. ChrisV

im trying to understand really

9. ChrisV

so if i take the original equation f(x)=-1/x

10. ChrisV

then i do the f(2)-f(1)

11. ChrisV

wait +f1)

12. ChrisV

im just confusing myself now lol

13. dumbcow

yeah f(2) -f(1)

14. ChrisV

-1/2-(-1/1)=1/2

15. ChrisV

thanks

16. dumbcow

welcome