Find the marginal cost to produce one more item if the
fixed cost is $400, the variable cost formula is 
,
and the current production quantity is 9 units.
| Foundations:
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Recall that the total cost,  , is the sum of the fixed and variable costs. Also, the marginal cost at Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle x_{0}}
units is defined to be the effective cost of the next unit produced, and is precisely Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C'(x_0)}
.
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| Solution:
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| Note that
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- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C(x)\,\,=\,\,\mbox{fixed costs + variable costs}\,\,=\,\,400+x^2+30x.}
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| The expression of the marginal cost is then
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- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C'(x)\,\,=\,\,2x+30.}
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| Finally, at a production quantity of 9 units, we have the marginal cost
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- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C'(9)\,\,=\,\,2(9)+30\,\,=\,\,48.}
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| Hence, the marginal cost at a production quantity of 9 units is $48.
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| Final Answer:
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| The marginal cost at a production quantity of 9 units is $48.
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