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lovekblue

  • 2 years ago

f(x) = ln x, [1, 8] Using mean value theorem, find all numbers c that satisfy the conclusion of the Mean Value Theorem.

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  1. myininaya
    • 2 years ago
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    \[f'(c)=\frac{f(b)-f(a)}{b-a}\]

  2. lovekblue
    • 2 years ago
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    I found my c to be 3.366 but the answer is wrong

  3. myininaya
    • 2 years ago
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    a=1 and b=8

  4. lovekblue
    • 2 years ago
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    yes, i know how to do it..but got it wrong.. don't know why

  5. myininaya
    • 2 years ago
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    Does it want an approximation?

  6. lovekblue
    • 2 years ago
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    it didn't say..so i'm thinking should the answer be an exact number

  7. lovekblue
    • 2 years ago
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    (Enter your answers as a comma-separated list. If it does not satisfy the hypotheses, enter DNE).

  8. lovekblue
    • 2 years ago
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    but then i think there is only 1 number c

  9. myininaya
    • 2 years ago
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    Well the number you put above is not the exact answer

  10. myininaya
    • 2 years ago
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    That is call an appoximation

  11. lovekblue
    • 2 years ago
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    how do get an exact number?

  12. myininaya
    • 2 years ago
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    So I assume you did the setup right because you got the approximation to the correct answer

  13. myininaya
    • 2 years ago
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    This is the setup you chose? \[\frac{1}{c}=\frac{\ln(8)-\ln(1)}{8-1}\]

  14. lovekblue
    • 2 years ago
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    yes

  15. myininaya
    • 2 years ago
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    We know ln(1) =? and 8-1=? So can you tell me what 1/c= Don't use your calculator

  16. lovekblue
    • 2 years ago
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    and then f'(c) = 1/c then solve for c

  17. lovekblue
    • 2 years ago
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    ln 1 = 0 8-1= 7

  18. myininaya
    • 2 years ago
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    Ok we have \[\frac{1}{c}=\frac{\ln(8)-0}{7}\] Do you know how to solve this for c?

  19. lovekblue
    • 2 years ago
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    ln 8/ 7 = 1/c c= 7/ln8

  20. myininaya
    • 2 years ago
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    right

  21. lovekblue
    • 2 years ago
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    ok thanks so much!

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