Question

The function C gives the cost (in dollars) to produce x gallons of fresh-squeezed lemonade.

What is the best interpretation for the following statement?
The value of the derivative of C at x = 10 is equal to 1.15.
A. At the time when 10 gallons of lemonade are produced, the costs increase by $1.15.
B. When the amount of lemonade produced is 10 gallons, the cost is increasing at a rate of $1.15 per gallon.
C. It costs $1.15 to produce 10 gallons of lemonade.
D. The cost of producing the lemonade increases at a rate of $1.15 per 10 gallons.

Answer 1

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Answer:

B. When the amount of lemonade produced is 10 gallons, the cost is increasing at a rate of $1.15 per gallon.

Explanation:

For C(x) = (dollar cost of producing x gallons of lemonade), the derivative C'(x) has units of dollars per gallon. It is the rate of change in cost when x gallons have been produced.

Then C'(10) is the rate of increase of cost, in dollars per gallon, when 10 gallons have been produced. (matches choice B)