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ChrisV

  • 2 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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  1. ChrisV
    • 2 years ago
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    f(x)=-1x^-1 -1(-1)x^-2 1/x^2

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

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

  4. ChrisV
    • 2 years ago
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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. :(

  5. dumbcow
    • 2 years ago
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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

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

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

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

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

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

  11. ChrisV
    • 2 years ago
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    wait +f1)

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

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

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

  15. ChrisV
    • 2 years ago
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    thanks

  16. dumbcow
    • 2 years ago
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    welcome

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