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Homework Help: Increasing function

  1. Jan 25, 2010 #1
    1. The problem statement, all variables and given/known data
    The largest interval on which the function f(x) = x2 + 4x + 2 is increasing is

    a. [0, ~)
    b. (-~, 0]
    c. [-2, ~)
    d. (-~, -2]
    e. (-2, ~)


    2. Relevant equations
    differentiation


    3. The attempt at a solution
    I am not sure the answer is (c) or (e). The condition that the function is increasing is f '(x) > 0 or f ' (x) [tex]\geq[/tex] 0?

    Thanks
     
  2. jcsd
  3. Jan 25, 2010 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Hi songoku! :smile:

    (have an infinity: ∞ and a geq: ≥ :wink:)
    "increasing" means > 0; ''non-decreasing" would be ≥ 0. :wink:
     
  4. Jan 25, 2010 #3
    Hi tiny-tim :smile:

    Thanks a lot !!! (again)
     
  5. Jan 25, 2010 #4

    Mark44

    Staff: Mentor

    But there's also the distinction between "increasing" - f'(x) >= 0 and "strictly increasing" - f'(x) > 0. And similar for decreasing vs. strictly decreasing.
     
  6. Jan 25, 2010 #5
    Hi Mark

    Hm...so what is the appropriate condition used for this question? Thanks
     
  7. Jan 25, 2010 #6

    Mark44

    Staff: Mentor

    Well, I would go with c) - [-2, inf)
     
  8. Jan 30, 2010 #7
    Hm...I think I'm with you Mark :smile:
     
  9. Jan 31, 2010 #8

    HallsofIvy

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    Science Advisor

    Songoku, the difficulty is that some textbooks use the "increasing", "nondecreasing" terminology while others use "increasing", "strictly increasing".

    You ought to check with our teacher or your textbook to make sure which your class is using.
     
  10. Jan 31, 2010 #9
    Hi HallsofIvy

    Ok, I'll do it. Thanks a lot for your suggestion :smile:
     
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