Not much explanation is needed to understand total costs. The only reason it is listed is to differentiate between Total Variable Cost and Total Cost.
Marginal costs are the changes in total cost when production increases by a single unit. Because at different levels of production the cost changes, marginal cost will also change as it is the cost of the next unit produced...
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Because at different levels of production the cost changes, marginal cost will also change as it is the cost of the next unit produced. In other words, marginal cost is the cost to produce the next unit. Hence, as production increases, so does the marginal cost.