Study Guide for Exam 1

• Functions
  • There will be very few questions on Chapter 1 as such, but a good understanding of the basic building blocks (polynomials, powers, exponentials, logs, and trig functions) and the basic ways of combining functions (especially composition) will be essential.
  • Logarithms and exponential growth: If you know the properties of log on page 40 and can solve the first 6 problems in section 1.7, you should be in good shape.
• Derivatives and formulas
  • Powers and polynomials
  • Exponentials, logarithms, and trig functions
  • Product rule
  • Quotient rule
  • Chain rule
  • Rule for f(x)^g(x)
  • Overall review: problems 25-36 on page 157.
• Derivatives and approximation
  • Estimate derivatives from table values (see 2.2: 5, 6, 15, 30).
  • Estimate derivatives from curves (see 2.1: 13, 14, 17). Especially, you should recognize the relation between increasing/decreasing functions and the sign of f'(x).
  • Estimate function values given known values and derivatives (see 2.3: 9--14).
  • Find the equation of the line tangent to the curve y = f(x) at a given point. (see 3.1: 38, 39).
• Interpretations of derivative
  • Find velocity given position as a function of time (see 3.1: 49, p. 157: 39).
  • Find acceleration, given velocity (or position, see above) as a function of time.
  • Find the slope of a curve (see tangent line problem above).
  • Compute rates of change, with correct units (for units, see 2.3: 1--7).
  • Find marginal cost, revenue, profit (see 2.5).
• Second derivatives
  • Recognize the relation between f''(x) and concavity.
  • Computing second derivatives is straightforward if you understand how to compute ordinary derivatives: just repeat the process twice.