Midterm 2 Review: M408C, 56250/55/60/80/85/90, Spring 2009

Covers Chapter 4 (sec. 1-4, 7, 9), and Chapter 5 (all)
 
Important topics:

  Fermat's Theorem, Extrema, & Critical Numbers (sec. 4.1-3)
  The Closed Interval Method (p. 209)
  The Mean Value Theorem (p. 216)
  Concavity & Inflection Points (sec. 4.3)
  Antiderivatives (sec. 4.9)

  Definition of the Integral (sec. 5.2)
  Properties of the Integral (p. 307-309)
  The Fundamental Theorem of Calculus I & II (p. 320)
  The Net Change Theorem (p. 327)
  U-Substitution (sec. 5.5)

Practice problems:

  4.1 Maximum and Minimum Values (#47,51,53,55)
  4.2 The Mean Value Theorem (#19,23,25)
  4.3 How Derivatives Affect ... (#9,11,13)
  4.4 Limits at Infinity (#11,15,19,29)
  4.9 Antiderivatives (#11,15,35,37)
  Chapter 4 Review (#1,3,5,9,11,53,55)

  5.2 The Definite Integral (#35,37,39,43)
  5.3 The Fundamental Theorem of Calculus (#9,11,13,19,25,29)
  5.4 Indefinite Integrals (#5,9,23,31)
  5.5 The Substitution Rule (#7,11,19,29,35,47)
  Chapter 5 Review (#15,17,19,27,33,35)

Suggestion: When you work the problems listed above, I strongly
suggest that you try to simulate the conditions of the midterm.  Copy
the problems listed from your textbook on to blank paper, with 4
problems per page.  Then take that paper and a pencil to the library,
leaving textbooks, laptops, ipods, and cellphones at home.  Sit by
yourself and try to work as many problems as possible, showing the
appropriate amount work, and giving explanations where necessary.  If
you get stumped on a given problem, move on to the next, and return to
it later.  When you can't work anymore problems, go home, check your
answers, and compute your practice midterm average.  If you're not
satisfied with the result, come to office hours.  (The last step
requires that you attempt the practice problems before Wednesday
morning.)

Disclaimer: This is not high school; the real midterm will not consist
of a subset of the practice problems with the numbers changed
slightly.