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Homework Help: Decreasing function

  1. Apr 19, 2005 #1
    the question is http://home.earthlink.net/~urban-xrisis/clip_image002.jpg [Broken]

    The answer is A but I dont understand why the function g would be decreasing when x=2 and x=-2
     
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Apr 19, 2005 #2
    The answer states between -2 and 2 not only when x=2 or x=-2. The function is decreasing because its derivative is negative. Where a derivative is negative the function is decreasing, where a derivative is positive the function is increasing. Think of your derivative as a slope, a negative slope means your function goes down from left to right(decreasing), and a positive slope means your function goes up from left to right(increasing).
     
  4. Apr 19, 2005 #3
    no, it states between -2 and 2 AND when they are equal. why?
     
  5. Apr 19, 2005 #4
    [tex] -2 \underline{<}x\underline{<}2[/tex]
    is different from:
    [tex] -2 < x < 2[/tex]

    why would the slope be decreasing at x=-2 and x=2 when the derivative is zero?
     
  6. Apr 19, 2005 #5
    I misunderstood your question sorry about that.The first derivative test(straight from a calc book) states:

    "Suppose that [tex]f[/tex] is continuous at each point of the closed interval [tex][a,b][/tex] and differentiable at each point of its interior [tex](a,b)[/tex]. if [tex]f'>0[/tex] at each point of *[tex](a,b)[/tex], then [tex]f[/tex] increases throughout *[tex][a,b][/tex].if [tex]f'<0[/tex] at each point of [tex](a,b)[/tex], then [tex]f[/tex] decreases throughout [tex][a,b][/tex]."

    *notice that they are using () meaning not including endpoints, however, after they use[] which means that the whole interval is increasing including the end points, this is by definition. As to why I don't remember right now, the calc book isn't helping much either, but i'm pretty sure the definition is right.
     
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