1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Decreasing function

  1. Apr 19, 2005 #1
    the question is here

    The answer is A but I dont understand why the function g would be decreasing when x=2 and x=-2
     
  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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?