Thread: please help sketch the graph

Sketch the graph of

Indicate the coordinates of important points clearly.

Hello, joey1!

Sketch the graph of: .
Indicate the coordinates of important points clearly.

By inspection, we see that the -intercepts are: .

Since has multiplicity 2, the graph is tangent to the -axis there.

If , then: . . . . y-intercept


Using calculus, we find that is a critical value,
. . and that is a maximum point.


The graph looks like this:

Code:

                      |
        *             |   (1,4)
                      |     o
         *            | *       *
          *      (0,2)o          *
            *       * |
    - - - - - - o - - + - - + - - o - -
             (-1,0)   |         (2,0)
                      |
                      |            *
                      |