Question

Math

Posted 6 months ago

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The function $C$ gives the cost, in dollars, to shred $w$ pounds of confidential documents of a company.
What is the best interpretation for the following statement?
$C^{\prime}(500)=80$
Choose 1 answer:
(A) The cost to shred documents, when the weight of the documents is 500 pounds, is increasing at a rate of $\$ 80$ per pound.
(B) The average cost to shred documents is $\frac{80}{500}$ dollars per pound.
(c) The cost to shred 500 pounds of documents is $\$ 80$.
D The cost to shred documents, when the weight of the documents is 500 pounds, is increasing at a rate of $\$ 80$.
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Answer from Sia

Posted 6 months ago

Solution by Steps

step 2

The derivative $C'(w)$ represents the rate of change of the cost with respect to the weight of the documents

step 3

The statement $C'(500) = 80$ means that when the weight of the documents is 500 pounds, the cost is increasing at a rate of $80 per pound

step 4

Therefore, the best interpretation is: "The cost to shred documents, when the weight of the documents is 500 pounds, is increasing at a rate of $80 per pound."

A

Key Concept

Derivative Interpretation

Explanation

The derivative of a function at a given point represents the rate of change of the function's value with respect to its input at that point.

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