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Homework Help: Graphing a function

  1. Feb 4, 2013 #1
    1. The problem statement, all variables and given/known data

    I should sketch function (x^2 + x -12)/(x-4).

    3. The attempt at a solution
    I have problem with first derivative i find it to be (x^2 - 8x +8)/(x-4)^2 with roots at 4 - 2√2, 4 + 2√2, and 4(we lose four because f is not defined at 4). Where at 4 - 2√2 f is at max and at 4 + 2√2 f is at min. But when i plug those two roots in f i find that when x 4 - 2√2 f is = 3.32 and when i plug 4 + 2√2 i find f to be 16.47. How come min is greater then max? Is that even possible?
  2. jcsd
  3. Feb 4, 2013 #2


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    Sure it is possible. They are only a local max and a local min. Start filling in your sketch of the rest of the function. You'll see what's happening.
  4. Feb 4, 2013 #3
    I figured it out by myself when i sketched graph. My professor didn't mention local max and min, he only talked about absolute. Thank you anyway.
  5. Feb 4, 2013 #4


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    Hi Government$! :smile:
    At x = 4 it goes off to infinity.

    The graph is effectively two unconnected graphs either side of x = 4, one with a maximum and one with a minimum …

    since they're unconnected, there's no reason why the maximum should be more than the minimum! :wink:
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