. On the current interval,
is a polynomial functrion, therefore it is differentiable; we have:
Let us look for points where the first derivative vanishes:
is in the domain where we work now. Moreover we have:
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