A function with parameters $a$ and $b$ is given. Describe the critical points and possible points of inflection of $f$ in terms of $a$ and $b$. Assume $a, b > 0$. $$f(x) = \dfrac{a}{x^2 + b^2}$$ Critical point:

Possible points of inflection: (two answers)
(smaller value)
(larger value)