Given the total cost function:
[tex]C(x)=550+130x-0.9x^2[/tex](a)
The marginal cost is the derivative of the cost function. Then, taking the derivative of C(x):
[tex]\begin{gathered} C^{\prime}(x)=0+130\cdot1-0.9\cdot2\cdot x \\ \Rightarrow C^{\prime}(x)=130-1.8x \end{gathered}[/tex](b)
The marginal cost of producing 55 golf clubs (x = 55 in the previous function):
[tex]\begin{gathered} C^{\prime}(55)=130-1.8\cdot55 \\ \Rightarrow C^{\prime}(55)=\text{ \$}31 \end{gathered}[/tex]