Acompany manufactures rope, and the total cost of producing r r feet of rope is c ( r ) c(r) dollars. what does it mean to say that c ( 2000 ) = 800 ? c(2000)=800? what are the units of c ′ ( r ) ? c′(r)? suppose that c ( 2000 ) = 800 c(2000)=800 and c ′ ( 2000 ) = 0.35 . c′(2000)=0.35. estimate c ( 2100 ) , c(2100), and justify your estimate by writing at least one sentence that explains your thinking. do you think c ′ ( 2000 ) c′(2000) is less than, equal to, or greater than c ′ ( 3000 ) ? c′(3000)? why? suppose someone claims that c ′ ( 5000 ) = − 0.1 . c′(5000)=−0.1. what would the practical meaning of this derivative value tell you about the approximate cost of the next foot of rope? is this possible? why or why not?