## anonymous 4 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. anonymous

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

2. anonymous

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

3. anonymous

how do i find the average rate?

4. anonymous

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. anonymous

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

6. anonymous

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

7. anonymous

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. anonymous

im trying to understand really

9. anonymous

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

10. anonymous

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

11. anonymous

wait +f1)

12. anonymous

im just confusing myself now lol

13. anonymous

yeah f(2) -f(1)

14. anonymous

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

15. anonymous

thanks

16. anonymous

welcome