Day 19 in Mat120

Today:

• Distribute Section 3.4 Worksheet (we'll talk about this next Tuesday - the quiz opportunity on Monday is for 3.5, which we'll be discussing then).

• Return 3.1 problem

• No quiz opportunity (opportunity for 3.5 on Monday).

• Roll

• No problems to collect.

• Questions on old stuff? (3.2 problems collected Monday; 3.3 problems extended due data: Wednesday)
  • From a quick read of the tests, I'd like to make one comment:

    Differentiability implies continuity, but continuity does not implies differentiability!

    Put another way:

    smoothness implies connectedness, but connectedness does not imply smoothness.

• Section 3.3:
  • section summary

  • worksheet study questions: questions?

  • Some sample proofs, and examples
    • constant
    • x
    • product
    • power - from conjecture to rule....
    Now we can differentiate any polynomial (e.g. #3)! Throw in the quotient rule, and you've got any rational function (e.g. #31)

Next time: Derivatives of trig functions