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Increasing and descreasing function question

  1. Feb 11, 2012 #1
    1. The problem statement, all variables and given/known data
    I've got two questions
    1.Find the intervals on which f increases and and the intervals on which f decreases.

    f(x)= x-cosx, 0≤x≤2∏

    2. Why is f(x) = -2sin2x - 2sinx = -2sinx (2cosx + 1)
    How can you factor 2cosx from the function on the left side?

    2. Relevant equations



    3. The attempt at a solution
    1.I get f '(x) = 1 + sinx, 0≤x≤2∏
    The answer says that it increases on [0,2∏] but I don't get it.
     
  2. jcsd
  3. Feb 11, 2012 #2

    tiny-tim

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    hi appplejack! :smile:
    learn your trigonometric identities

    sin2x = 2sinxcosx :wink:
    1 + sinx is always ≥ 0, isn't it? :smile:
     
  4. Feb 11, 2012 #3
    Thanks for your help but I think I need to work on trig. Could you explain why 1 + sinx is always ≥ 0?
     
  5. Feb 11, 2012 #4

    tiny-tim

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    draw it! :biggrin:
     
  6. Feb 11, 2012 #5
    I'm weak on trig. For 1 + sinx, does it shift the graph upward by 1 because y intercept is 1
    when x=0? And the graph of sine goes up and down. That's why I doubt that the function increases all the time. I know that I'm wrong but I'm still wondering why.
     
  7. Feb 11, 2012 #6

    tiny-tim

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    1 + sinx is the derivative, it doesn't matter if it goes up and down, so long as it doesn't become negative :wink:
     
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