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Math Help - Info for function f(x)=x^2/(x-1)

  1. #1
    rocktguy
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    Info for function f(x)=x^2/(x-1)

    First, thanks for any help. It's been a couple of decades since I have tried any college math, but I'm back in school and I'm attempting to finish a degree and trying to understand how to get some info on the function f(x)= x^2/(x-1).
    1. All extrema
    2. Inflection points
    3. Intercepts
    4. Asymptotes.
    5. Show concave structure and note any discontinuities

    I can simply get the results using Maple 11 software, but can't understand how to get there.

    Thanks !
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  2. #2
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    Quote Originally Posted by rocktguy View Post
    First, thanks for any help. It's been a couple of decades since I have tried any college math, but I'm back in school and I'm attempting to finish a degree and trying to understand how to get some info on the function f(x)= x^2/(x-1).
    1. All extrema
    2. Inflection points
    3. Intercepts
    4. Asymptotes.
    5. Show concave structure and note any discontinuities

    I can simply get the results using Maple 11 software, but can't understand how to get there.

    Thanks !
    Extrema = local max/min/absolute max or min

    1. f'(x)=\dfrac{2x(x-1)-(1)(x^2)}{(x-1)^2} = \dfrac{x(x-2)}{(x-1)^2}

    To find local min or max is when the derviative is zero. so...

    0=x(x-2) x=0,2 then you look at the interval less then zero, bewteen 0-1,1-2, and >2 to see if its max or min. You plug in numbers in each of these intervals to see if the function is neg. or pos. In this case, at x=0 it is a local min. and at x=2 it is a local max.
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