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 $\$ 80$.

Question

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 $\$ 80$.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ The function $C$ gives the cost, in dollars, to shred $w$ pounds of confidential documents of a company. ‖ ‖ 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.⚹◊What is the interpretation of $C'(500) = 80$ in the context of the cost function $C(w)$ for shredding confidential documents?⍭ Generate me a similar question◊

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