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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]
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]

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ChrisV
 3 years ago
Best ResponseYou've already chosen the best response.0f(x)=1x^1 1(1)x^2 1/x^2

ChrisV
 3 years ago
Best ResponseYou've already chosen the best response.01/(1)^2=1 1/(2)^2=2 instantaneous rates: f'(1)=1 ; f'(2)= 1/4

ChrisV
 3 years ago
Best ResponseYou've already chosen the best response.0how do i find the average rate?

ChrisV
 3 years ago
Best ResponseYou've already chosen the best response.0i 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. :(

dumbcow
 3 years ago
Best ResponseYou've already chosen the best response.1think of slope between the 2 endpoints avg rate = f(2) f(1) / 21 = 1/2 (1) / 1 = 1/2

dumbcow
 3 years ago
Best ResponseYou've already chosen the best response.1or more technically using calculus \[avg rate = \frac{1}{ba}\int\limits_{a}^{b}f'(x) dx = \frac{f(b) f(a)}{ba}\]

ChrisV
 3 years ago
Best ResponseYou've already chosen the best response.0im trying to understand really

ChrisV
 3 years ago
Best ResponseYou've already chosen the best response.0so if i take the original equation f(x)=1/x

ChrisV
 3 years ago
Best ResponseYou've already chosen the best response.0im just confusing myself now lol
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