Day 29 in Mat121

Today:

• Hand out directed reading handout, Section 4.4 (html) (pdf)

• Sorry: forgot to take the quiz home to grade yesterday....

• Section 4.2: Extrema
  • Rolle's theorem works backwards: we deduce the existence of a critical point from an extremum:
    

  • Examples:
    • #2, p. 188
    • (see Galloping Gertie)
    • Others?

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

• Section 4.3:
  • Mean Value Theorem:

    

    Notice that Rolle's theorem is a special case (or corollary) of the Mean Value Theorem, yet the MVT is proven via Rolle's theorem!

  • First Derivative Test:

    

  • Examples:

  • Questions over the Directed reading handout, Section 4.3 (html) (pdf)?

• Great calculus demos