A List of Topics for Midterm 2

• Finding the tangent line to a given point
• Setting up equation to find horizontal tangent line of explicit functions
• Derivatives of trigonometric functions (3.4)
• Computing limits using the fact lim(sin x)/x = 1 as x goes to 0 (3.4) (L'Hospital usually works here too)
• Recognizing function compositions and using the Chain Rule (3.5)
• Implicit differentation for implicit functions (3.6)
• Setting up equations to find horizontal tangents of implicit functions (3.6)
• Derivatives of inverse trigonometric functions (3.6)
• Computing higher derivatives (3.7)
• Derivatives of ln and log (3.8)
• Knowing when and how to use logarithmic differentiation (3.8)
• Derivatives of hyperbolic and inverse hyperbolic functions (3.9)
• Related rates: setting up variables and equations, then implicit differentiation (3.10)
• Using linear approximation by choosing appropriate f, x, a (3.11)
• Differentials; computing maximum possible error, relative error, % error (3.11)
• Knowing when and how to apply the closed interval method (4.1)
• Statement of Rolle's Theorem, Mean Value Theorem; finding c satisfying their conclusions (4.2)
• Proving an identity using Corollary 4.2.7 (4.2)
• Finding critical points (4.1) and local max/min using sign of f '(x) (4.3)
• f ''(x), concavity, inflection points (4.3)
• Second derivative test (4.3)
• When and how to use L'Hospital Rule for the limit of a quotient (4.4)
• Rewriting indeterminate products, differences, powers, then using L'Hospital (4.4)
• Curve sketching checklist (the above and absolute max/min, horizontal, vertical, slant asymptotes) (4.5)

• Review homework problems and make sure you know how to do them
  • Check the solution manual at office hours
• Ask questions in section on Tuesday or at office hours
• Practice taking the other version of quizzes you did not take
  • The quizzes given in section were 1B, 2B, 3A, 4A, 5A, 6A, 7A
• Take the practice midterm (to be up soon)
• Try the worksheet on 4.1-4.3 given in section October 21 (mainly try 1 and 2)
  • Solutions here