1. ## Minimum

f(x)=abs(x+2)+abs(x-1)-2 will this graph have a minimum? it decreases and remains constant for a small interval can I say these are minimums if they are in a consecutive line?

Thank you

2. Yes, it just means it has infinite minima (there are an infinite number of points in the line)

3. Hello, IDontunderstand!

$f(x)\:=\:|x+2|+ |x-1|-2$
Will this graph have a minimum?

It decreases and remains constant for a small interval . . . .
then increases.
Can I say these are minimums if they are in a consecutive line?
I say Yes . . .

The graph looks something like this:

Code:
                |
*       |       *
*      |      *
*     |     *
*   1|    *
* * * * *
|
- - - + - + - + - - - -
-1   |   1
|

The graph has a minimum value: . $f(x) \,=\,1$
. . which occurs for $|x|\,\leq 1$