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MATH 131-505 Spring 2015 Review II c Wen Liu 2.6 • know how to interpret the average rate of change and instantaneous rate of change on graphs (as shown on page 1) • know the slope of the tangent line is the same as the derivative of f (x) at x = a, i.e. f 0 (a) 2.7 • given a graph f (x), be able to graph f 0 (x) • know when f (x) fails to be differentiable • be able to use the limit definition to find f 0 (x) 2.8 • know the definitions of local maximum and local minimum • know everything on page 1 from the notes and be able to use it (to get all information about f (x) from f 0 (x)), i.e. problem 3 on page 2 • be able to interpret f 0 and f 00 , like problem 2 3.1 • be able to find the derivatives using the rules listed on page 1 • be able to find the equation of tangent line that is parallel to a given line or to find the equation of the normal line. • know where a tangent line is horizontal 3.2: be able to find the derivatives using the product rule and quotient rule 3.3 • know how to find the derivative of trig functions • know how to find the tangent line at a point to a curve 3.4: know how to use chain rule to find the derivatives 3.7: know the formula on page 1 and use it to find the derivatives 3.8 • given a distance/position function s(t), know the velocity v(t) = s0 (t) and the acceleration a(t) = v 0 (t) • be able to analysis the motion of a particle if s(t) is given 3.9: know how to use linearization to approximate a number review quizzes/notes Page 1 of 1