# Financial Mathematics Question

By considering the functions $x(e^\frac{\delta}{x} - 1)$ and $x(1-e^\frac{-\delta}{x})$ and their derivatives with respect to x for $x \geq 1$ and $\delta > 0$ show that $i^{(p)} > i^{(p+1)}$ and $d^{(p+1)} > d^{(p)}$ when p is an integer greater than zero.