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Reciprocal of a quadratic function - math help

  1. Oct 7, 2009 #1
    1. The problem statement, all variables and given/known data

    For the function y = 1 / ((x-1)^2)
    what is:

    a) the sign of slope
    b) change in slope (increasing or decreasing)

    for the interval x > 1

    Here is the graph:

    http://img7.imageshack.us/img7/3204/12491454.jpg [Broken]



    2. Relevant equations
    None


    3. The attempt at a solution

    I said the slope is negative and the change in slope is increasing (going closer to zero) as the values of x increase. But the answer in the text says its negative but the slope is decreasing. I compared to a few other text questions and it goes back and forth on the same shape on other questions, am i missing something?

    thanks.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Oct 7, 2009 #2

    berkeman

    User Avatar

    Staff: Mentor

    For x>1, the slope is very steep at first, and levels out as x gets bigger and bigger. What does that say about whether the slope is increasing or decreasing? Remember the definition of the slope (it's the tangent to the curve, right?).
     
  4. Oct 7, 2009 #3
    looking at the value of the slope initially for small values of X its a large negative number. Then as x increases the slope becomes a smaller negative figure. This means its approaching zero, therefore increasing in my eyes. This is also the way the teacher showed us, the book flops back and forth with answers in other questions. Is my thinking correct?
     
  5. Oct 7, 2009 #4

    berkeman

    User Avatar

    Staff: Mentor

    Ah, I see the ambiguity now. Hmm. You could say that the magnitude of the slope is decreasing. Is the word "magnitude" used by the book maybe?
     
  6. Oct 7, 2009 #5

    Mark44

    Staff: Mentor

    Matt1234,
    I agree with you. For x > 1, the slope is negative, and it is increasing. I don't know if you know about the 2nd derivative yet, but for your graph on the same interval, y'' > 0, which is equivalent to saying that y' is increasing.
     
  7. Oct 7, 2009 #6
    cool, thats what i needed to hear. :) i am familiar with calclus and the senond derivative, this is jsut a simple functions math course, cacl is next semister, lol. From high school to graduating 3 years of college then back to high school then 4 years of university. :)
     
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