Day 22 in Mat121

Today:

• Friday: first Mathematics Lunch will be held, from 11:30am to 1:30pm, in ST 343. Come even if you're just thinking about majoring or minoring in math.

• Don't forget: exam 2 tomorrow, over derivatives (through 3.7).

• Return Quiz
  • Solution
  • It was hard! Actually just messy. Define functions to clean up your mess. I was looking for the following:
    1. Would you be able to rewrite things so that only the product and quotient rules would be necessary?
    2. Especially, would you get your laws of exponents rigth?
    3. Would you try for the chain rule?
    4. Would you evaluate the derivative using your calculator? Then you have a target.
    5. Did you define important quantities? "Let...."
  • Problems:
    • "equality abuse"
    • getting the chain rule right, even if you use it illegally!;)

• Section 3.7: The Chain Rule
  • Examples:
    • #68, p. 153

  • Questions over the Directed reading handout, Section 3.7 (html) (pdf)?

• What questions do you have in advance of tomorrow's test?

• Section 3.8: Implicit Differentiation
  • First of all, notice that we suddenly see graphs failing the vertical line test. These are not the typical "functions of a single variable" we usually encounter, but rather include "branches" which individually can be treated as such.

  • Favorite example: the circle

  • We can still compute slopes of tangent lines, however, as we've been led to expect.

  • Implicit differentiation movie (two thumbs up!)

  • Other Examples:
    • #41, 160
    • #44, 160

  • Questions over the Directed reading handout, Section 3.8 (html) (pdf)?

• Great calculus demos (and more on implicit differentiation).