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The graph of the function is given; Draw the graph of f'

  1. Jan 28, 2014 #1
    1. The problem statement, all variables and given/known data

    The graph of the function f is given, Draw the graph of f'
    The graph looks like that of a parabola extending continuously upwards to the left and the right.


    2. Relevant equations

    lim f(x+ delta(x)) - f(x)
    delta x -> 0 delta(x)

    or power rule nX^n-1

    3. The attempt at a solution
    I have been accustomed to numerical derivatives and using the limit process or power rule to find the answer. Here I am given a graph (from what I see has direct points at (0,0), (1,1), (2,4), (-1,-1), and (-2,4) ). What I would like to know is how to approach the problem.
    I tried to reference a problem in my textbook similar to this problem and I see that the parabola's lowest point is onto of (4,0) and the answer in the book then uses this point in the answer (sort of) with x=4. I would like to know, since my problem is similar to the practice problem which way i would draw the line since my parabola is right in the middle of the graph unlike the practice problem (number 41).

    I appreciate the help / guidance in advanced.
     

    Attached Files:

  2. jcsd
  3. Jan 28, 2014 #2
    For all of these you first need to determine f(x) from the graphs given. Use your intuition and basic understanding of different functions to do so. Then take the derivative of the function, f'(x), using whatever means you are comfortable with. And then simply graph f'(x).
     
  4. Jan 28, 2014 #3
    So in this instance the graph already given looks like x^2 so I could simply use the power rule and obtain 2x as the the f'. Then graph 2x. Is that correct?
     
  5. Jan 28, 2014 #4
    Exactly, you got it! :smile:
     
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