E2M155reviewfa06 - M155 Exam 2 Review Sheet 2.5 Derivatives...

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M155 Exam 2 Review Sheet 2.5 – Derivatives of Sums, Powers, and Polynomials • Terminology Power Function Polynomial • Use binomial theorem to compute powers of sums • Constant Rule d dx c f ( x ) ( 29 = c d dx f ( x ) ( 29 • Sum Rule d dx f ( x ) + g ( x ) ( 29 = df dx + dg dx • Power Rule d dx x n ( 29 = nx n - 1 2.6 – Derivatives of Products and Quotients • Terminology Rational Functions • Product Rule d dx f ( x ) g ( x ) ( 29 = f ( x ) dg dx + g ( x ) df dx OR f ( x ) g ( x ) ( 29 = f ( x ) g ( x ) + g ( x ) f ( x ) • Quotient Rule d dx f ( x ) g ( x ) = g ( x ) df dx - f ( x ) dg dx g ( x ) [ ] 2 OR f ( x ) g ( x ) = g ( x ) f ( x ) - f ( x ) g ( x ) g ( x ) [ ] 2 2.7 – The Second Derivative, Curvature, and Acceleration • Terminology Concave Up Concave Down Acceleration Point of Inflection Second Derivative • Find the second derivative of functions • Find all points of inflection (point where second derivative is zero and changes sign) • Determine the curvature of a function • If ′′ f ( a ) < 0
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