Determine whether he curve ha a tangent at the indicated point. If it does, give its slope. If not, explain why not?

f(x)=\left\{\begin{array}{rr}x&\ 2-2x-x^2 {if }x\ge0\\ -x&\2x-2{if } x > 0\end{array}\right. there is the messed up LaTex if anyone could/will/may :) etc, answer this. thank you!

The above is at x= 0. The second inequality is supposed to have an > or = sign.

Ah.

I couldn't get it. :( The LaTEx, I mean.

Here it is in math:

f(x)= 2-2x-x^2, x < 0

piecewise 2x+ 2, x > or = 0.

Graphola!

http://www.geocities.com/onlychristislife/graph56.jpg

I circled the point which I think they are talking about for the tangent.

If there isn't one, figuring out the slope will be messy. However its done.

Thanks!