Is marginal cost different from extra cost?

Question

I have been reading this resource which talks about why derivatives can be used to find the marginal cost.

https://www.dummies.com/education/math/calculus/how-to-determine-marginal-cost-marginal-revenue-and-marginal-profit-in-economics/

I am slightly confused about a statement referring to marginal cost and extra cost. They write "If you look very closely at the right side of the above figure, you can see that the extra cost goes up to the curve, but that the marginal cost goes up a tiny amount more to the tangent line, and thus the marginal cost is a bit more than the extra cost".

Are they stating that the marginal cost is different from the extra cost? Isn't that incorrect as the marginal cost is the extra cost from producing one more unit of a good? Or is marginal cost separate from the extra cost?

is it saying that marginal cost is different from extra cost?

Answer 1

In this graph they use marginal cost to describe a sort of linear approximation of the change in the cost function $C(x)$ at some point $x_0$, that is $$ MC_{x_0}(x) = (x-x_0) \cdot \frac{\partial C(x_0)}{\partial x}. $$ This is indeed not the usual way the term marginal cost is used.

Answer 2

I think it's because marginal cost is the area of the triangle under the tangent line, since marginal cost is the derivative of the cost function. But since the cost curve is shown to be convex, the actual cost of increasing production by one unit would have less area.