Let us look for points where the first derivative vanishes:

Actually, only is in the domain where we work now. Moreover we have:

Thus, decreases on and increases on .

What about differentiability on the left at 0?

It follows that

hence, the function is differentiable on the left at 0 at its first left-derivative at 0 is equal to 0.

We have one limit to compute here:

Does the graph of have an oblique asymptote here?

therefore the graph of has no oblique asymptote, but a parabolic branch for in neighborhood of .

Noah Dana-Picard 2007-12-28