This function is defined on .
The function is the product of the natural logarithm by a monomial, hence it is differentiable on its domain. We have:
Now let us check the limits of at the open ends of its domain.
Does the graph of the function have an oblique asymptote:
Now, let us check how the graph looks like near the origin: We have
Now let us compute the second derivative:
The graph of is displayed in Figure 3.
Noah Dana-Picard 2007-12-28