Understanding Absolute Value Sign in Derivative

[sony]

Hi

So I am 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)

 

[sony]

Hints anyone...?

 

[saltydog]

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

and:

|x-1|=-(x-1)\quad\text{for}\quad x&lt;1

Thus your expression represents this function:

y(x)=<br /> \left\{<br /> \begin{array}{rcl}<br /> (x-1)e^x &amp; \mbox{for} &amp; x\geq 1 \\ <br /> -(x-1)e^x &amp; \mbox{for} &amp; x&lt;1<br /> \end{array}\right.<br />

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.