Thread: Graphing

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

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

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

Thanks Captain is any one able to graph this and send it to me

Hello, nath_quam!

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



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

has x-intercepts:

As . . . The graph rises to the right.

As . . . 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:

The graph rises to the right and to the left.

We find that is an inflection point
. . and there is a minimum at

Code:

        *     |
         *    |                     *
           *  |
              *                    *
      --------+---o--------------o---
              |     *           *
              |      *       *
              |         * *
              |

Thanks but with the second graph wouldn't the point 5/2 be a maximum

Originally Posted by Soroban

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

The graph rises to the right and to the left.

We find that is an inflection point
. . and there is a minimum at

Code:

        *     |
         *    |                     *
           *  |
              *                    *
      --------+---o--------------o---
              |     *           *
              |      *       *
              |         * *
              |

The co-efficient of is negative, so the graph should be
the other way up.

Nice ASCII art work as usual

RonL