Suppose that the cost function for a product is given by $C(x)=0\mathrm{.}002x^3+6x+7,263.$ Find the production level $($that is$,$ the value of $x)$ that will produce the minimum average cost per unit $\frac{?}{\text{b}\text{a}\text{r}}(C)(x)$

The production level that produces the minimum average cost per unit is $x=($Round to the nearest whole number as needed.$)$