# Homework Help: Solve |x-1|e^x

1. Sep 28, 2005

### sony

Hi

So Im a little confused about the absolute value sign here. Is the derivative right:

[x-1/|x-1|]e^x + |x-1|e^x

But what do I do when I set this to zero? Do I get two expressions, one for x>1 and one for x<1 ? (thus removing the absolute value signs)

2. Sep 29, 2005

### sony

Hints anyone...?

3. Sep 29, 2005

### saltydog

$$|x-1|=x-1\quad\text{for}\quad x\geq 1$$

and:

$$|x-1|=-(x-1)\quad\text{for}\quad x<1$$

Thus your expression represents this function:

$$y(x)= \left\{ \begin{array}{rcl} (x-1)e^x & \mbox{for} & x\geq 1 \\ -(x-1)e^x & \mbox{for} & x<1 \end{array}\right.$$

and so the derivative will represent two functions likewise but will not exist at x=1. Try plotting this conditional function and you'll see what I mean.