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Math Help - Graphing

  1. #1
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    Cool Curve Sketching Challenge

    What do the graphs
    a) P(x) = x(3x+2)(x-3)(x+2)

    and

    b) P(x) = ((1-x)^3)(x-3)

    look like and there keys points
    Last edited by nath_quam; June 14th 2006 at 08:47 PM.
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  2. #2
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    Quote Originally Posted by nath_quam
    What do the graphs
    a) P(x) = x(3x+2)(x-3)(x+2)

    look like and there keys points
    It goes to infinity as x goes to +/- infinity.

    It has four distince roots at 0, -2/3, 3 and -2.

    It has a local max/min between each pair of roots.

    RonL
    Last edited by CaptainBlack; June 14th 2006 at 11:15 PM.
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  3. #3
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    Quote Originally Posted by nath_quam
    b) P(x) = ((1-x)^3)(x-3)
    It goes to -infinity as x goes to +/- infinity

    It has a root of multiplicity 3 at x=1 (it is negative as x approches 1 from
    below, is tangent to the axis at x=1, and is positive
    as x moves away from 1 above), and a simple root at x=3

    It has a maximum between the roots.

    RonL
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  4. #4
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    Thanks Captain is any one able to graph this and send it to me
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  5. #5
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    Hello, nath_quam!

    What do the graphs looks like and what are their key points?

    a)\;P(x) \:= \:x(3x+2)(x-3)(x+2)

    1-x)^3(x-3)" alt="b)\; P(x) \:= \1-x)^3(x-3)" />
    a)\;P(x) \:=\:x(3x+2)(x-3)(x+2) has x-intercepts: -2,\;-\frac{2}{3},\;0,\;3

    As x\to\infty,\;\;P(x) \to \infty . . . The graph rises to the right.

    As x\to-\infty,\;\;P(x) \to \infty . . . The graph rises to the left.

    You should be able to sketch the graph now . . .
    Code:
                          |                 *
          *               |
                          |                *
           *           ** |
        ----o-------o-----o---------------o--
             *     *      | *            *
                **        |    *       *
                          |        * *
                          |
    You can use the derivative to locate the exact positions
    . . of the maximum and the two minimums.



    1-x)^3(x-3)" alt="b)\;\;P(x)\:=\1-x)^3(x-3)" /> has x-intercepts: 1,\;3

    The graph rises to the right and to the left.

    We find that (1,0) is an inflection point
    . . and there is a minimum at x = \frac{5}{2}
    Code:
            *     |
             *    |                     *
               *  |
                  *                    *
          --------+---o--------------o---
                  |     *           *
                  |      *       *
                  |         * *
                  |
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  6. #6
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    Maximum

    Thanks but with the second graph wouldn't the point 5/2 be a maximum
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  7. #7
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    Quote Originally Posted by Soroban

    1-x)^3(x-3)" alt="b)\;\;P(x)\:=\1-x)^3(x-3)" /> has x-intercepts: 1,\;3

    The graph rises to the right and to the left.

    We find that (1,0) is an inflection point
    . . and there is a minimum at x = \frac{5}{2}
    Code:
            *     |
             *    |                     *
               *  |
                  *                    *
          --------+---o--------------o---
                  |     *           *
                  |      *       *
                  |         * *
                  |
    The co-efficient of x^4 is negative, so the graph should be
    the other way up.

    Nice ASCII art work as usual

    RonL
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