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anonymous

  • 5 years ago

MVT of f(x)=e^(-2x)

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  1. anonymous
    • 5 years ago
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    hey, how's it going?

  2. anonymous
    • 5 years ago
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    I know the answer to this problem, but have gotten stuck when plugging in the values of a,b into the derivative

  3. anonymous
    • 5 years ago
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    Good thank you

  4. anonymous
    • 5 years ago
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    f'(x) = -2e^(-2x) Sorry Interval [0,3] a @ 0 = 1 b @ 3 = e^-6

  5. anonymous
    • 5 years ago
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    so what are you stuck on?

  6. anonymous
    • 5 years ago
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    is this definitely the question as written, it doesn't look like the answer is going to be very "pretty"

  7. anonymous
    • 5 years ago
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    f(x)=e^(-2x) Find all numbers that satisfy the conclusion of the Mean Value Theorem

  8. anonymous
    • 5 years ago
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    on the closed interval [0,3]

  9. anonymous
    • 5 years ago
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    ok so what are you stuck on

  10. anonymous
    • 5 years ago
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    Getting the answer of -1/2ln[1/6(1-e^-6)]

  11. anonymous
    • 5 years ago
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    do you know the formula of the mean value theorem? maybe you can tell me what part you're having trouble with

  12. anonymous
    • 5 years ago
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    f'(c)=f(b)-f(a)/b-a or f(b)-f(a) = f'(c)(b-a)

  13. anonymous
    • 5 years ago
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    do you want to tell me the steps you took and maybe i can see where you made a mistake?

  14. anonymous
    • 5 years ago
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    I am not clear on how to incorporate the deriviative which is -2e^-2x using my a and b into this...

  15. anonymous
    • 5 years ago
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    walking myself in circles

  16. anonymous
    • 5 years ago
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    c is what you want to find

  17. anonymous
    • 5 years ago
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    you have b and a and f(b) and f(a)

  18. anonymous
    • 5 years ago
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    so f '(c) = -2e^(-2c) = you have the formula

  19. anonymous
    • 5 years ago
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    the theorem means that there is an x-value c somewhere in the interval that makes the formula true

  20. anonymous
    • 5 years ago
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    ok. so then would it e^(-6)-1=-2e^(-2c)(e^-6-1)

  21. anonymous
    • 5 years ago
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    this being the average rate of change between these points, right

  22. anonymous
    • 5 years ago
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    sorry last part (3-0)

  23. anonymous
    • 5 years ago
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    looks right i think with your correction

  24. anonymous
    • 5 years ago
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    Sometimes it helps to talk it out. Thanks a million!

  25. anonymous
    • 5 years ago
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    did you end up getting the right answer?

  26. anonymous
    • 5 years ago
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    Working through it now. YES!

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