To solve for the total cost of producing the following numbers of cups of coffee:
[tex]\begin{gathered} C(x)=0.097x \\ \end{gathered}[/tex]where
[tex]\begin{gathered} x=nu\text{mber of cups of coff}e \\ C(x)=total\text{ cost }in\text{ dollars of producing x cups} \end{gathered}[/tex](a) The total cost of producing 1000 cups =
[tex]\begin{gathered} C(x)=0.097x \\ x=1000 \\ C(x)=1000(0.097)=\text{ \$97} \end{gathered}[/tex](b) The total cost of producing 1001 cups =
[tex]\begin{gathered} C(x)=0.097x \\ x=1001 \\ C(x)=1001(0.097)=\text{ \$97}.097 \end{gathered}[/tex](c) The marginal cost for any cup = $0.097
marginal cost can be found by taking the derivative of the function
[tex]\begin{gathered} C(x)=0.097x \\ C^1(x)=0.097=\text{ \$0.097} \end{gathered}[/tex]