Question 78478
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I am confused on these type of problems, please help. 
If f(x)=x(x+3)(x-1), use interval notation to give all values of
   x where f(x)>0
a. (-3,1)
b. (-3,0)<font face = "symbol">È</font>(1,<font face = "symbol">¥</font>)
c. (1,3)
d. (0,1)<font face = "symbol">È</font>(3,<font face = "symbol">¥</font>)

-------------------------------------

f(x) = x(x + 3)(x - 1)

The critical values are 0, -3 and 1

Mark those on a number line:

---------o-----------o---o--------
-5  -4  -3  -2  -1   0   1   2   3 

That divides the number line into 4 parts:

 (-<font face = "symbol">¥</font>,-3), (-3,0), (0,1), (1,<font face = "symbol">¥</font>) 

Make this chart:

     interval | (-<font face = "symbol">¥</font>,-3) | (-3,0) | (0,1) | (1,<font face = "symbol">¥</font>) |  
test value, t |    -4   |   -1   |   .5  |    2  |
         f(t) |   -20   |    4   | -.875 |   10  |
 sign of f(t) |     -   |    +   |    -  |    +  |


Since we are looking for the solution set of f(x) > 0
we are looking for the intervals in which the sign of f(x)
is positive. These are (-3,0) and (1,0), so the solution set
is

                  (-3,0) <font face = "symbol">È</font> (1,<font face = "symbol">¥</font>)

which is choice b.

Edwin</pre>