Business Calculus Cheat Sheet, Cheat Sheet of Business Mathematics

Business Calculus (MTH 270) Quick Reference

Calculus I (MTH 173) and Business Calculus (MTH 270) are similar in the material covered, including limits, first and

second derivative tests, and optimizations.

The major differences between Calculus I and Business Calculus are:

● Business Calculus applies calculus to various business-related problems.

● Business Calculus DOES NOT cover derivatives or anti-derivatives of trig functions or inverse trig functions.

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Total Profit = P(x) = R(x) - C(x)

● Marginal Cost, Revenue and Profit

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Marginal Cost = C’(x)

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Marginal Revenue = R’(x)

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Marginal Profit = P’(x) = R’(x) - C’(x)

○ The marginal cost is the instantaneous rate of change of the cost relative to the level of production, 𝑥.

● Exact Cost, Revenue and Profit

○ The exact cost, revenue or profit are the cost, revenue or profit of producing the (𝑥 + 1)st item.

○ 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐶𝑜𝑠𝑡 = 𝐶(𝑥) = 𝐶(𝑥)

○ 𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐶𝑜𝑠𝑡 = 𝐶′(𝑥) = 𝑑

○ 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑅𝑒𝑣𝑒𝑛𝑢𝑒 = 𝑅

○ 𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑅𝑒𝑣𝑒𝑛𝑢𝑒 = 𝑅

Elasticity of Demand (p. 226)

● Relative Rate of Change

○ 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑅𝑎𝑡𝑒 𝑜𝑓 𝐶ℎ𝑎𝑛𝑔𝑒 = 𝑑

○ 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑅𝑎𝑡𝑒 𝑜𝑓 𝐶ℎ𝑎𝑛𝑔𝑒 = 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑅𝑎𝑡𝑒 𝑜𝑓 𝐶ℎ𝑎𝑛𝑔𝑒 𝑥 100%

● Elasticity of Demand

○ Price, 𝑝

○ Demand, 𝑥 = 𝑓(𝑝)