Determine the intervals on which the following function is concave up or concave down. Identify any inflection points.

$f(x)=x^4-2x^{3}3$

Determine the intervals on which the given function is concave up or concave down. Select the correct choice below and fill in the answer box$($es$)$ to complete your choice.

$($Simplify your answer. Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.$)$

$$

The function is concave up on and concave

A$.$ down on $.$

b$.$ The function is concave up on

C$.$ The function is concave down on