Exam 2 Review Topics, Fall, 2008
Basics: Derivatives, tangent line approximation, linearization, differentials, critical points (2 types), inflection points, local extrema, absolute extrema, increasing and decreasing, concave down and concave up, mean values.
Techniques: All differentiation rules: summation rule, scalar product rule, product rule, quotient rule, chain rule. Implicit differentiation. Tangent line approximation, equation of tangent line, linearization, differentials. Finding critical points, finding absolute extrema on closed intervals, 1st derivative test for local extrema. Determining the signs of derivative functions over intervals segmented by critical points, determining increasing and decreasing intervals of functions. Determining the signs of the second derivatives of functions, determining the interval of concave down and concave up and points of inflection. Sketch graphs of functions featuring local extrema, intervals of increasing and decreasing, intervals of concave down and concave up, and points of inflection. Mean Value Function Theorem.
Elementary Functions: Derivative of power functions, exponential functions, logarithmic functions, trigonometric functions, inverse trigonometric functions
Calculator Skills: Sketch graphs, tracing intersection points and roots, finding numerical limits
Miscellaneous Techniques: quadratic formula for roots, factorization of a^2-b^2, a^3-b^3, long division, multiply and divide to maintain and transform quantities. Basic forms and shapes of polynomials: linear function, parabola, cubic polynomials, definitions of trigonometric functions and their inverse functions, exponential functions, and logarithmic functions, basic identities of trigonometric functions including double angle and half angle formulas, basic rules, identities, and limiting properties as x → ∞ for exponential and logarithmic functions, special values of trigonometric functions and their inverses, and special values of exponential and logarithmic functions
Partial Review Problems: All homework, quiz, lecture example problems, and sample exams