Study Guide for Exam 2

• Maxima and Minima
  • Know how to find the critical points of a function.
  • Know what is meant by a local maximum or minimum and how critical points are the only candidates.
  • Be able to solve global maximum and minimum problems, like 4.3: 13.
• Interpretations and applications of Definite Integrals
  • Accumulated change (5.1: 3, 4, 8; 5.4: 5, 8, 9, 10)
  • Total distance travelled (5.1: 2, 13; 5.4: 14, 18)
  • Area under a curve or between two curves (5.3)
  • Bioavailability (5.4: 19, 20)
  • Cost and revenue in terms of MC and MR (5.5: 4-8)
  • Averages: know the formula for the average of a function over an interval (6.1).
  • Supply and demand will NOT be on the exam.
  • Remember that with integration, units multiply (5.4: 2, 3, 4).
• Computing Definite Integrals
  • Estimating from table values (5.2: 7-10)
  • Estimating from graphs (1, 2, 12-14)
  • Computing from the fundamental theorem of calculus. We don't have a good stock of examples, but any 7.1 problem can be turned into a definite integration problem by sticking in values of a and b. Here are some examples: What is the integral of 3x from x=2 to x=4? What is the integral of t¹² from t=0 to t=1? What is the integral of x²+1 from x=0 to x=3?
• Computing indefinite integrals (also known as antiderivatives)
  • Know how to handle antiderivatives of sums, differences, and constant multiples.
  • Know how to integrate all powers of x including x^-1.
  • Know how to use the above two items to integrate polynomials
  • Know the integrals of exponential functions and sine and cosine.
  • You should be able to handle any problem 7.1: 25-49.