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# The cost, C (in dollars), to produce g gallons of a chemical can be expressed as C = f(g). Using units, explain the meaning of the following statements in terms of the chemical: (a) f(200) = 1300 (b) f'(200) = 6

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The cost, $C$ (in dollars), to produce $g$ gallons of a chemical can be expressed as

\begin{align*} C & = f(g) \end{align*}

##### (a)

It is given that

\begin{align*} f(200) & = 1300 \end{align*}

The above equation means that to produce 200 gallons of chemical the cost is 1300 dollars.

##### (b)

It is given that

\begin{align*} f'(200) & = 6 \end{align*}

The above statement says that after producing 200 gallons, the cost of production is increasing at the rate of 6 dollars/gallon.

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