Day 17 in Mat121

Today:

• Note: quiz tomorrow over definition of the derivative

• directed reading handout, Section 3.6 (html) (pdf)

• Sections 3.2 and 3.3: The Derivative Function, and important rules

  Examples:

  • #61, p. 118
  • #63, p. 118
  • #64, p. 118

• Sections 3.5: Higher Derivatives
  • "Little fleas have littler fleas upon their backs to bite em / and littler fleas have littler fleas / and so on ad infinitum."

  • Functions that are differentiable have derivative functions, that are functions and may be differentiable and hence have derivative functions, and so on ad infinitum.

  • There's nothing especially novel about the calculation of higher derivatives.
    • Using the calculator to compute higher derivative

  • They do provide something new in the way of interpretation of the behavior of a curve.
    • Second derivatives give us inflection
    • Degree one polynomials have zero second derivatives.
    • The most important case: the quadratic
      • bowls versus umbrellas
      • Galileo and the second derivative of the position function s(t)=s_o+v_ot - 16t²
    • #33, p. 141

  • Note on homework problem #40, p. 141: remove the label "Distance" from the graph, then answer the question.