Question

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]

Answer 1

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

Answer 2

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

Answer 3

how do i find the average rate?

Answer 4

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. :(

Answer 5

think of slope between the 2 endpoints

avg rate = f(2) -f(1) / 2-1
= -1/2 -(-1) / 1
= 1/2

Answer 6

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

Answer 7

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

Answer 8

im trying to understand really

Answer 9

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

Answer 10

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

Answer 11

wait +f1)

Answer 12

im just confusing myself now lol

Answer 13

yeah f(2) -f(1)

Answer 14

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

Answer 15

thanks

Answer 16

welcome