Marginal cost function is a derivative of the cost function. To get the cost function, you need to do the opposite, that is, integrate.
Profits are maximized when marginal costs equals marginal revenue because fixed costs are now spread over a larger amount of revenue. This means that total cost per unit declines and profits...
equal to marginal revenue
a person
Marginal Cost = Marginal Revenue, or the derivative of the Total Revenue, which is price x quantity.