Consider $g(x)=4x-72x^3-2x^2$

Determine the intervals on which $g$ is concave down.

$9$ is concave down on: $$

$g$ is concave down nowhere.

Determine the intervals on which $g$ is concave up$.$

$g$ is concave up on: $$

$g$ is concave up nowhere.

Determine the value and location of any inflection point of $g.$ Enter the solution in $(x,g(x))$ form. If multiple solutions exist, use a comma$-$separated list to enter the solutions.

$g$ has an inflection point at: $$

$g$ has no inflection point.