This function is defined on .
The function is the composition of a rational function on the exponential; thus, it is differentiable on its domain. We have:
Let us compute the limits of at the open ends of the domain:
As the exponential function with basis has as its limit at , we need some lagberaic work. We have:
At , we need to compute one-sided limits:
Let us now compute the second derivative of :
We display the graph of in Figure 4.
Noah Dana-Picard 2007-12-28