"Marginal cost is never equal to variable costs." Please explain why this is false?

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):

C'(x)=dC/dx