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ChrisV
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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
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

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

ChrisV Group TitleBest ResponseYou've already chosen the best response.0
1/(1)^2=1 1/(2)^2=2 instantaneous rates: f'(1)=1 ; f'(2)= 1/4
 2 years ago

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

ChrisV Group TitleBest ResponseYou've already chosen the best response.0
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. :(
 2 years ago

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

ChrisV Group TitleBest ResponseYou've already chosen the best response.0
so basically f(1)f(2)?
 2 years ago

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

ChrisV Group TitleBest ResponseYou've already chosen the best response.0
im trying to understand really
 2 years ago

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

ChrisV Group TitleBest ResponseYou've already chosen the best response.0
then i do the f(2)f(1)
 2 years ago

ChrisV Group TitleBest ResponseYou've already chosen the best response.0
im just confusing myself now lol
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.1
yeah f(2) f(1)
 2 years ago

ChrisV Group TitleBest ResponseYou've already chosen the best response.0
1/2(1/1)=1/2
 2 years ago
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