The cost of manufacturing the 401st yard of fabric is C(401) − C(400) = − 22,400 ≈ , which is approximately C'(400)

It seems like there's some information missing from your question. The cost of manufacturing the 401st yard of fabric is given by the difference C(401) - C(400), but you've written that this equals -22,400. This would suggest that producing the 401st yard somehow reduces costs, which doesn't make sense in the context of a manufacturing process.

Also, you've mentioned C'(400), which suggests that we're dealing with a derivative here. In the context of cost functions, C'(400) would represent the marginal cost of producing the 401st yard of fabric.

However, without more information or context, it's difficult to provide a more accurate or helpful response. Could you please provide more details or clarify your question?