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Math Help - Graphing Help???

  1. #1
    Newbie
    Joined
    May 2007
    Posts
    5

    Graphing Help???

    I am supposed to a graph the function f(x) given the following characteristics:

    • f(0)= 4 and f(6)= 0
    • f '(x)< 0 if x< 2 and x> 4
    • f '(2) does not exist and f '(4)=0
    • f '(x)>0 if 2< x< 4
    • f ''(x)< 0, x 2
    I understand the first one gives the points (0,4) and (6,0) but am confused with the other four. Please Help
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  2. #2
    Super Member

    Joined
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    Lexington, MA (USA)
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    Hello, mathkid2007!

    Graph the function f(x) given the following characteristics:

    (1)\;f(0)= 4\text{ and }f(6)= 0
    (2)\;f '(x)< 0 \text{ if }x< 2\text{ and }x> 4
    (3)\;f '(2)\text{ does not exist and }f '(4)=0
    (4)\;f '(x)>0\text{ if }2< x< 4
    (5)\;f ''(x)< 0,\;x \neq 2

    (1) gives us two points: (0,4) and (6,0).
    Code:
              |
             4*
              |
              |
              |
          - - + - - - - - - - - - - - * - - -
              |                       6
              |

    (2) says the slope is negative for x < 2 and x > 4.
    Code:
              |
              |
          *   |
             4*
              |  *              *
              |    *               *
              |     *                * 6
          - - + - - - - + - - - + - - * - - -
              |         2       4
              |                         *
              |

    (3) says there is a vertical asymptote at x = 2
    . . and a horizontal tangent at x = 4.
    Code:
              |      x=2
          *   |       :
             4*       :
              |  *    :     --*--
              |    *  :       :   *
              |     * :       :      * 6
          - - + - - - + - - - + - - - * - - -
              |      *:       4
              |       :                *
              |      *:
              |       :

    (4) says the slope is positive on (2,4).
    (5) says the graph is always concave down.
    Code:
              |      x=2
              |       :
          *   |       :
             4*       :
              |  *    :       *
              |    *  :   *   :   *
              |     * :  *    :      * 6
          - - + - - - + * - - + - - - * - - -
              |      *:2      4
              |       :*               *
              |      *:
              |       :

    . . . There!

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