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Mastering Derivatives: Functions and Formulas

Learn how to calculate 1st and 2nd derivatives with respect to X for various functions. Explore examples and solutions in this insightful guide.

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Mastering Derivatives: Functions and Formulas

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  1. Think Break #3 • What are the 1st and 2nd derivatives with respect to X of the following functions? • Q = 4 + 15X – 7X2 • p = 2(5 – X – 3X2) – 8X - 15 • p = p(b0 + b1X + b2X2) – rX – K

  2. Think Break #3: Answers • Q = 4 + 15X – 7X2 1st: dQ/dX = 15 – 14X 2nd: d2Q/dX2 = – 14 • p = 2(5 – X – 3X2) – 8X – 15 1st: dp/dX = 2(– 1 – 6X) – 8 = – 10 – 12X 2nd: d2p/dX2 = – 12 • p = p(b0 + b1X + b2X2) – rX – K 1st: dp/dX = p(b1 + 2b2X) – r 2nd: d2p/dX2 = p(2b2) = 2pb2

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