You can
put this solution on YOUR website!Hello,
I always make a table.
On the top line, I put he zeros of he funcion. In this case: 2 and 3
Then I a look at the sign of (x-2) and (x-3) while I variate x.
Let's take a look at this table:
x ->_____________2_________3_______________________
(x-2) = - - - - - - - - 0 + + + + + + + + + + + + + + +
(x-3) = - - - - - - - - - - - - - - - - -0 + + + + + + + + +
________________________________________
f(x)= + + + + + + + + 0 - - - - - - - - - 0 + + + + + + + + +
If x < 2 , then (x-2) is negative: put a '-'sign
if x = 2, then (x-2) = 0
If x > 2, then x-2 is positive: put a '+'sign
Do the same for x-3
Now think in vertical lines when looking to the table.
In the last line, you first take over the zeros. Then you put a + or a - sign. The last line is the mutiplication of the (x-2) and (x-3) line.
This means that: - and - gives a +
+ and + gives a +
+ and - gives a -
- and + gives a -
We know read from the last line that f(x) is < 0 between 2 and 3.
The answer: f(x) < 0 if x is in ]2,3[
Here's a visual plot:
Greets,
Scriptor
(