please help sketch the graph

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• Mar 23rd 2010, 05:44 AM
joey1
please help sketch the graph
Sketch the graph of $\displaystyle y=(1+x)^2 (2-x)$

Indicate the coordinates of important points clearly.
• Mar 23rd 2010, 07:22 AM
Soroban
Hello, joey1!

Quote:

Sketch the graph of: .$\displaystyle y\:=\:(1+x)^2 (2-x)$
Indicate the coordinates of important points clearly.

By inspection, we see that the $\displaystyle x$-intercepts are: .$\displaystyle x = \text{-}1,\;2$

Since $\displaystyle x=\text{-}1$ has multiplicity 2, the graph is tangent to the $\displaystyle x$-axis there.

If $\displaystyle x = 0$, then: .$\displaystyle y = 2$ . . . y-intercept $\displaystyle (0,2)$

Using calculus, we find that $\displaystyle x = 1$ is a critical value,
. . and that $\displaystyle (1,4)$ is a maximum point.

The graph looks like this:
Code:

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