Microeconomic question with cost curves

5. Cost Curves Consider the following cost function c(q) = q2 + F. Where F > 0. (a) Find the: variable cost function, fixed cost function, average variable cost function, average fixed cost function, average cost function and marginal cost function. (b) Show that as q - oo, the average cost function converge to the average variable cost function converge. (c) Assuming F = 1, draw on the same graph the marginal cost function, average cost function and average variable cost function. What's the relation between the marginal cost function and the slope of the average cost function