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Homework Help: Derivatives graph help

  1. Sep 24, 2004 #1
    Help me plz! :confused:

    graph.png

    For the function f whose graph is given, arrange the following numbers in increasing order and explain why:
    • 0
    • f'(2)
    • f(3) - f(2)
    • 1/2[f(4) - f(2)]
     
  2. jcsd
  3. Sep 24, 2004 #2
    0 is undefined...on an asymptote

    out of f'(2), f(3) - f(2) and 1/2[f(4) - f(2)]

    increasing order:

    1/2[f(4) - f(2)]
    f(3) - f(2)
    f'(2)
     
  4. Sep 24, 2004 #3
    but why? :confused:
     
  5. Sep 24, 2004 #4
    a. 0
    b. f'(2)
    c. f(3) - f(2)
    d. 1/2[f(4) - f(2)]

    0 is the smallest and I'll explain why in a second.
    f(3) - f(2) can be rewritten as (f(3) - f(2)) / (3-2). This slope is only a tiny fraction smaller than b because if you notice the slope is gradually decreasing as x gets larger. 1/2(f(4)-f(2)) can be rewritten as (f(4)-f(2))/(4-2). This looks like the average slope over that interval which you will notice was slightly less than c (which is in turn slightly less than b)

    b, c, and d are positive though because the graph increases from 0-infinity apparently so a is the smallest. Ok I pretty much did all the work for you whoops.
     
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