Determine the intervals on which the given function is concave up or concave down and find the points of inflection.

$f(x)=2x{e}^{-9x}$

$($Use symbolic notation and fractions where needed. Give your answer as a comma separated list of points in the form in the form $(**,**).$ Enter DNE if there are no points of inflection.$)$

points of inflection:

Determine the interval on which $f$ is concave up$.$

$($Use symbolic notation and fractions where needed. Give your answer as interval in the form $(**,**).$ Use the symbol $$ for infinity, $$ for combining intervals, and an appropriate type of parenthesis $"(",")","[","]"$ depending on whether the interval is open or closed. Enter $\frac{O}{?}$ if the interval is empty.$)$

xin $$

Determine the interval on which $f$ is concave down.

$($Use symbolic notation and fractions where needed. Give your answer as interval in the form $().$ Use the symbol oo for infinity, $$ for combining intervals, and an appropriate type of parenthesis $"(",")","[","]"$ depending on whether the interval is open or closed. Enter $\frac{O}{?}$ if the interval is empty.$)$