Usually, this statement would be true. Marginal cost refers to the cost of producing the next unit of output. By contrast, variable costs are all the variable costs associated with all the output up to and including the last unit. So the marginal cost will usually be smaller than the variable cost because it only refers to the variable costs associated with making the *last* unit.
However, there is one time when the two things will be equal. That is for the *first* unit produced. When you go from 0 units produced to 1 unit produced, the marginal cost of the 1st unit will be equal to the total variable costs.
Marginal cost function is the first derivative of the cost function.
Marginal cost expresses how much are changing costs, when production of a good increases (usually with an infinitesimal unit). This value may be, of course, even negative. Marginal cost intersects the average costs always their minimum point.If marginal costs decreasing, the point of intersection of two curves is the point of maximum average costs.
If marginal costs are higher than average costs, without fixed costs, is reached the minimum level of profitability. If a firm produces below the minimum threshold of profitability, is not good to produce more, because it not even cover variable costs.
It's better when marginal costs exceed average costs, including fixed costs. From this perspective, the optimal threshold of profitability, producer gets profit.
Marginal costs formula(first derivative of cost function depending on x):