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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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: