If the cost function for a commodity is
\[
C(x)=\frac{1}{90} x^{3}+2 x^{2}+2 x+16 \text { dollars }
\]
find the marginal cost $ \overline{M C} $ at $ x=9 $ units. (Round your answer to two decimal places.) $ \overline{M C}=\$ 407 / 10 $
Tell what the marginal cost predicts about the cost of producing 1 additional unit.
The cost of producing 1 additional unit is $ \$-139 / 30 $.
Tell what the marginal cost predicts about the cost of producing 2 additional units.
The cost of producing 2 additional units is $ \$ 1501 / 30 $.
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Calculate the cost of producing 1 additional unit and 2 additional units: \(\Delta C_{1} = MC(9)-MC(10), \Delta C_{2} = MC(9)-MC(11)

Steps

Step 1 ：Differentiate the cost function: $ MC(x) = \frac{dC}{dx} = \frac{1}{30} x^{2} + 4x + 2$

Step 2 ：Find the marginal cost at x=9: $ MC(9) = \frac{1}{30}(9)^{2} + 4(9) + 2 $

Step 3 ：Calculate the cost of producing 1 additional unit and 2 additional units: \(\Delta C_{1} = MC(9)-MC(10), \Delta C_{2} = MC(9)-MC(11)