anonymous
  • anonymous
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]
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
f(x)=-1x^-1 -1(-1)x^-2 1/x^2
anonymous
  • anonymous
1/(1)^2=1 1/(2)^2=2 instantaneous rates: f'(1)=1 ; f'(2)= 1/4
anonymous
  • anonymous
how do i find the average rate?

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anonymous
  • 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. :(
dumbcow
  • dumbcow
think of slope between the 2 endpoints avg rate = f(2) -f(1) / 2-1 = -1/2 -(-1) / 1 = 1/2
anonymous
  • anonymous
so basically f(1)-f(2)?
dumbcow
  • dumbcow
or more technically using calculus \[avg rate = \frac{1}{b-a}\int\limits_{a}^{b}f'(x) dx = \frac{f(b) -f(a)}{b-a}\]
anonymous
  • anonymous
im trying to understand really
anonymous
  • anonymous
so if i take the original equation f(x)=-1/x
anonymous
  • anonymous
then i do the f(2)-f(1)
anonymous
  • anonymous
wait +f1)
anonymous
  • anonymous
im just confusing myself now lol
dumbcow
  • dumbcow
yeah f(2) -f(1)
anonymous
  • anonymous
-1/2-(-1/1)=1/2
anonymous
  • anonymous
thanks
dumbcow
  • dumbcow
welcome

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