Business Calculus Cheat Sheet, Cheat Sheet of Business Mathematics

Download Business Calculus Cheat Sheet and more Cheat Sheet Business Mathematics in PDF only on Docsity! 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. If you have taken Calculus I, you are able to assist a student in Business Calculus, and vice versa. Marginal Analysis (p. 163) ● Cost, Revenue and Profit ○ Total Cost = C(x) ○ Total Revenue = R(x) ○ Total Profit = P(x) = R(x) - C(x) ● Marginal Cost, Revenue and Profit ○ Marginal Cost = C’(x) ○ Marginal Revenue = R’(x) ○ 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. Exact Cost = C(x+1) - C(x) ○ The marginal cost approximates the cost of the (𝑥 + 1)st item produced. Marginal Cost ≈ Exact Cost C’(x) ≈ C(x+1) - C(x) ● Average Cost, Revenue and Profit ○ 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐶𝑜𝑠𝑡 = 𝐶̅(𝑥) = 𝐶(𝑥) 𝑥 ○ 𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐶𝑜𝑠𝑡 = 𝐶̅′(𝑥) = 𝑑 𝑑𝑥 𝐶̅(𝑥) ○ 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑅𝑒𝑣𝑒𝑛𝑢𝑒 = ?̅?(𝑥) = 𝑅(𝑥) 𝑥 ○ 𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑅𝑒𝑣𝑒𝑛𝑢𝑒 = ?̅?′(𝑥) = 𝑑 𝑑𝑥 ?̅?(𝑥) ○ 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑃𝑟𝑜𝑓𝑖𝑡 = ?̅?(𝑥) = 𝑃(𝑥) 𝑥 ○ 𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑃𝑟𝑜𝑓𝑖𝑡 = ?̅?′(𝑥) = 𝑑 𝑑𝑥 ?̅?(𝑥) Elasticity of Demand (p. 226) ● Relative Rate of Change ○ 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑅𝑎𝑡𝑒 𝑜𝑓 𝐶ℎ𝑎𝑛𝑔𝑒 = 𝑑 𝑑𝑥 𝑙𝑛[𝑓(𝑥)] = 𝑓′(𝑥) 𝑓(𝑥) ○ 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑅𝑎𝑡𝑒 𝑜𝑓 𝐶ℎ𝑎𝑛𝑔𝑒 = 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑅𝑎𝑡𝑒 𝑜𝑓 𝐶ℎ𝑎𝑛𝑔𝑒 𝑥 100% ● Elasticity of Demand ○ Price, 𝑝 ○ Demand, 𝑥 = 𝑓(𝑝) ○ 𝐸𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦 𝑜𝑓 𝐷𝑒𝑚𝑎𝑛𝑑 = 𝐸(𝑝) = − 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒 𝑜𝑓 𝑑𝑒𝑚𝑎𝑛𝑑 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒 𝑜𝑓 𝑝𝑟𝑖𝑐𝑒 ○ 𝐸(𝑝) = − 𝑝 𝑓′(𝑝) 𝑓(𝑝)