The cost, in dollars, of producing $x$ gallons of detergent is given by
$C (x) = 350 + 20 x 0.08 x^{2} + 0.0004 x^{3}$
What is a formula for the marginal cost function $C^{'} (x)$

C (x) = 200.16 x^{2} + 0.0012 x^{2}

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C (x) = 200.16 x + 0.0012 x^{2}

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C (x) = 20 x 0.16 x + 0.0012 x^{2}

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C (x) = 20 x 0.16 x^{2} + 0.0012 x^{2}

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Solution

The correct option is B $C (x) = 200.16 x + 0.0012 x^{2}$
$c^{'} (x) = \frac{d}{d x} (c (x))$
$= 2 \times (100 + 0.8) x + 3 \times 0.0004 x^{2}$
$= 200.16 x + 0.0012 x^{2}$

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\frac{d C}{d x}

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