1. ## scatch the graph

Hello,

I need help with the analysis of the following function.
Before to draw it need to find intersection points, min. max. asymptotes, discuss the domain, convexity/concavity by the usage of the second derivative test.. Having difficuloties with the following function:
f= x^x

and

f=e^(-x^2)

any help is welcome.

Thanks,

2. f = x^x = e^(xln(x))

f' = e^(xln(x))(ln(x)+1)

f' = x^x(ln(x)+1)

I'll let you take it from here

3. thank you,
but the problem for me is to define the functions find D.O (is it defined for the negative numbers?), more is the limit of x^x when x approaches zero 1 ? and what is is zero when x approaches -infinity ??

4. x^x is only defined for x> 0 so it makes no sense in talking asbout the limit
as x goes to - infinity since x is never negative

You would have to know L Hopital's rule in order to show x^x->1 as
x ->0 :

write y = lim (x^x)
x ->0
lny = lim xln(x)
x->0

lim xln(x) = lim ln(x)/(1/x) = lim -x = 0

lny = 0

y = e^0 = 1

i.e lim x^x = 1 as x goes to 0

Without L'hopital's rule you'll have to rely on a graph