Day 18 in Mat121

Today:

• Note: quiz today over the definition of the derivative

• 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.

  • 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
    • Surfing derivatives
    • Derivatives of sine
    • Second derivatives of sine
    • Derivative puzzles

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

• Section 3.6: Trigonometric Derivatives
  • Derivative of cosine from the definition, and trig identities
  • Problems:
    • #23, p. 145
    • #27, p. 145
    • #47, p. 146