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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
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  1. ChrisV Group Title
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    f(x)=-1x^-1 -1(-1)x^-2 1/x^2

    • 2 years ago
  2. ChrisV Group Title
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    1/(1)^2=1 1/(2)^2=2 instantaneous rates: f'(1)=1 ; f'(2)= 1/4

    • 2 years ago
  3. ChrisV Group Title
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    how do i find the average rate?

    • 2 years ago
  4. ChrisV Group Title
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    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
  5. dumbcow Group Title
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    think of slope between the 2 endpoints avg rate = f(2) -f(1) / 2-1 = -1/2 -(-1) / 1 = 1/2

    • 2 years ago
  6. ChrisV Group Title
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    so basically f(1)-f(2)?

    • 2 years ago
  7. dumbcow Group Title
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    or more technically using calculus \[avg rate = \frac{1}{b-a}\int\limits_{a}^{b}f'(x) dx = \frac{f(b) -f(a)}{b-a}\]

    • 2 years ago
  8. ChrisV Group Title
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    im trying to understand really

    • 2 years ago
  9. ChrisV Group Title
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    so if i take the original equation f(x)=-1/x

    • 2 years ago
  10. ChrisV Group Title
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    then i do the f(2)-f(1)

    • 2 years ago
  11. ChrisV Group Title
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    wait +f1)

    • 2 years ago
  12. ChrisV Group Title
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    im just confusing myself now lol

    • 2 years ago
  13. dumbcow Group Title
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    yeah f(2) -f(1)

    • 2 years ago
  14. ChrisV Group Title
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    -1/2-(-1/1)=1/2

    • 2 years ago
  15. ChrisV Group Title
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    thanks

    • 2 years ago
  16. dumbcow Group Title
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    welcome

    • 2 years ago
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