Use a graph below of $f(x) = \ln(2 x^2 + 1)$ to estimate the $x$-values of any critical points and inflection points of $f(x)$.

critical points (enter as a comma-separated list): $x =$
inflection points (enter as a comma-separated list): $x =$

Next, use derivatives to find the $x$-values of any critical points and inflection points exactly.
critical points (enter as a comma-separated list): $x =$
inflection points (enter as a comma-separated list): $x =$