## ChrisV Group Title 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] 2 years ago 2 years ago

1. ChrisV Group Title

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

2. ChrisV Group Title

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

3. ChrisV Group Title

how do i find the average rate?

4. ChrisV Group Title

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 Group Title

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

6. ChrisV Group Title

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

7. dumbcow Group Title

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 Group Title

im trying to understand really

9. ChrisV Group Title

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

10. ChrisV Group Title

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

11. ChrisV Group Title

wait +f1)

12. ChrisV Group Title

im just confusing myself now lol

13. dumbcow Group Title

yeah f(2) -f(1)

14. ChrisV Group Title

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

15. ChrisV Group Title

thanks

16. dumbcow Group Title

welcome