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.

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

Step-by-step 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)

answer: .75 km

step-by-step explanation:

a) at most means it can cost $12 or less

so the inequality sign would be ≤

you would then need to multiply the number of toppings by the 0.35 for each one and add it to the cost of the cheese pizza.

the equation would be 9.99 + 0.35x ≤ 12

b) using the above equation:

9.99 + 0.35x ≤ 12

subtract 9.99 from each side:

0.35x ≤2.01

divide both sides by 0.35:

x ≤ 2.01 / 0.35

x ≤5.74

at most you could have 5 toppings.

the 5 topping pizza would cost: 0.35 x 5 = 1.75 + 9.99 = $11.74