Day 28 in Mat121

Today:

• Hand out directed reading handout, Section 4.3 (html) (pdf)

• Quiz over related rates

• Section 4.1: linear approximations and applications
  • Examples:
    • #8, p. 179
    • #23, p. 180

  • Questions over the Directed reading handout, Section 4.1 (html) (pdf)?

• Section 4.2: Extrema
  • Extreme values: maxes and mins, globally and locally:

  • Critical points:

  • Finding extrema:
    1. We know they're there:
    2. Critical points are critically important:
    3. For absolutes, we need to check endpoints:
    4. Rolle's theorem works backwards: we deduce the existence of a critical point:

  • Examples:
    • Preliminary questions: 1, 2, p. 188
    • #2, p. 188

  • Questions over the Directed reading handout, Section 4.2 (html) (pdf)?

• Great calculus demos (and more on linearization).