Suppose a firm's short$-$run cost function is C $($q$)=500+300$q $3$q$2+1/2$q$3.$

Determine the fixed costs, the variable costs, the average costs, average variable costs, the average fixed costs as well as the marginal costs. At what output level does the marginal cost curve cross the average cost curve? Give a verbal $($intuitive$)$ explanation!