Let $\displaystyle f(x)$ be defined for all real numbers except at $\displaystyle x=0$ such that whose derivatives are given by

$\displaystyle f'=\frac{-e^\frac{1}{x}}{x^2}$ and $\displaystyle f"=\frac{e^\frac{1}{x}(2x+1)}{x^4}$

a) Find the interval(s) of concave upward/concave downward of $\displaystyle f(x)$

b) At what value(s) of x does the function $\displaystyle f(x)$ have point(s) of inflection?