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Finding increasing/decreasing intervals of an equation using critical points?

  1. Mar 30, 2012 #1
    1. The problem statement, all variables and given/known data

    Hi I have an equation as follows:
    f(x) = (2x-2.3)/(2x-5.29)^2

    what i got for the derivative was:
    f'(x) = (-1.38-4x)/(2x-5.29)^3


    2. Relevant equations
    f(x) = (2x-2.3)/(2x-5.29)^2
    f'(x) = (-1.38-4x)/(2x-5.29)^3

    3. The attempt at a solution

    what i got for the critical point is -0.345, but then the question asks when the function is increasing and decreasing, expecting 3 intervals. if there is only one critical point, i can see two intervals but not three. am i missing a critical point here? i have excluded x = 2.645 because it is not a part of the domain.
     
  2. jcsd
  3. Mar 30, 2012 #2

    ehild

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    It is a vertical asymptote there, and the derivative might change sign.

    ehild
     
    Last edited: Mar 30, 2012
  4. Mar 30, 2012 #3
    but if i include it it shows that the function is increasing over intervals (-infinity,-0.345) U (2.645,+infinity) and decreasing on (-0.345,2.645). however i know that -0.345 is a relative minimum, and if those intervals hold, it becomes a relative maximum...
     
  5. Mar 30, 2012 #4

    ehild

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    Check the sign of the derivative.

    ehild
     
  6. Mar 30, 2012 #5
    i already know the answer is that the function f is decreasing on (-infty, -0.345 ) U (2.645 ,+infty ) and increasing on ( -0.345 , 2.645).
    im just not sure at how they arrived to it in my profs notes >.<

    we do the table method where its like:

    -0.345 2.645
    ------------------------------------
    -1.38-4x | - 0 + | +
    (-2x-5.29)^3 | - | - 0 +
    f'(x) | + | - | +
    f(x) | go up | go dwn| go up

    my final f(x) ends up being the opposite of what its supposed to be :s im not sure what im doing wrong here. any help is much appreciated.
     
  7. Mar 30, 2012 #6

    ehild

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    f'(x) = (-1.38-4x)/(2x-5.29)^3

    You know that the function is increasing when its derivative is positive.

    Is f' positive or negative, if x>2.645? Say, x=3. Is -1.38-4x negative or positive? Is 2x-5.29 negative or positive?

    ehild
     
  8. Mar 30, 2012 #7
    Ohhh just got the mistake. Great, thank you for your help and patience!
     
  9. Mar 30, 2012 #8

    ehild

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    You are welcome. :smile:

    ehild
     
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