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Math Help - Derivative graph

  1. #1
    Blueazulim06
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    Derivative graph

    Hi, I have this graph of a function but it doesn't give the equation for the function. The question wants me to graph the derivative but I don't know how. I am able to count where the points are so can anyone help me?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Blueazulim06 View Post
    Hi, I have this graph of a function but it doesn't give the equation for the function. The question wants me to graph the derivative but I don't know how. I am able to count where the points are so can anyone help me?
    Recall that the derivative of a function at a point is the slope of the tangent line to the curve at that point. So sketch the tangent line at a point on the graph and measure the slope of that line. That will give you the value of the derivative at that point.

    A handy trick to remember while you are doing this is that any point where the function has a relative maximum or minimum is going to be a point where the derivative graph crosses (or perhaps touches) the x-axis. (Because the derivative is zero there.) The same comment holds for inflection points as well if you are practiced enough to be able to spot those.

    -Dan
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  3. #3
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    Hello, Blueazulim06!

    Topsquark gave you the best advice.
    Let me try to make it clearer . . .


    I have this graph of a function, but not the equation for the function.
    The question wants me to graph the derivative.

    Suppose your graph looks like this:
    Code:
                    *
              *           *
    
           *                 *
    
          *                   *                 *
    
                               *               *
    
                                  *         *
                                        *

    Estimate the slope at a number of points.
    Code:
                   m=0
           m=1      -*-    m=-1
              *           *
            /               \
       m=2 *                 * m=-2
          /                   \
          *                   *                   *
    
                               *                 * m=2
                                 \             /
                             m=-1 *           * m=1
                                   \   -*-   /
                                       m=0

    Those are the values we plot on the "derivative graph".
    Code:
          |
         2+   *                       *
          |
          |
         1+      *                 *
          |
          |
        - + - - - - * - - - - - * - -
          |
          |
        -1             *     *
          |
          |
        -2+               *
          |

    Hope this helps . . .

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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Soroban View Post
    Hello, Blueazulim06!

    Topsquark gave you the best advice.
    Let me try to make it clearer . . .


    Suppose your graph looks like this:
    Code:
                    *
              *           *
     
           *                 *
     
          *                   *                 *
     
                               *               *
     
                                  *         *
                                        *
    Estimate the slope at a number of points.
    Code:
                   m=0
           m=1      -*-    m=-1
              *           *
            /               \
       m=2 *                 * m=-2
          /                   \
          *                   *                   *
     
                               *                 * m=2
                                 \             /
                             m=-1 *           * m=1
                                   \   -*-   /
                                       m=0
    Those are the values we plot on the "derivative graph".
    Code:
          |
         2+   *                       *
          |
          |
         1+      *                 *
          |
          |
        - + - - - - * - - - - - * - -
          |
          |
        -1             *     *
          |
          |
        -2+               *
          |
    Hope this helps . . .
    Thanks Soroban. I still haven't gotten any graphing software.

    -Dan
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