Day 71 in Mat120

• Apologies to Angela for calling her algorithm "dumb"! It's no reflection on her, of course. Oftentimes the best algorithm to use is a dumb algorithm....

Today:

• No new worksheet - never again let there be a worksheet!

• Return 7.6 problems
  • #22 - note difference between sinh^-1(x) and 1/sinh(x)!

  • #54 - don't forget your constants; don't forget to change back to x; don't switch to exponential functions to integrate!

• No quiz opportunity - never again let there be a quiz opportunity!

• Problems 7.7 collection opportunity.

• Questions on old stuff?

• Section Review:
  • Today we'll look at early stuff (differentiation); tomorrow, middle stuff (integration); Friday, recent stuff.

  • There's old final stuff on-line

  • Review (part I of III)
    • Function Zoo
      • known animals
      • Especially - linear functions
    • Unknown animals
      • Transformations
      • Compositions
      • Inverses
      • New types
        • Exponentials/Logarithms
        • Hyperbolic trig functions
    • Limits
    • Derivatives

  • Types of Problems:
    • Study of a function
      • Domain and Range
      • Intercepts (e.g. roots)
      • Symmetry
      • Asymptotes (including slant)
      • Continuity
      • Differentiability
      • Increasing/Decreasing intervals
      • Concavity and Inflection
      • Extrema
      • Graph it!
    • Calculate derivatives using
      • Limit definition
      • Formulas (product, chain, etc.)
    • Using derivatives
      • To find extrema
      • Especially: Optimization problems
      • Matching derivatives (to create smoothness, e.g. when should a pilot start descent?)
      • Higher derivatives
    • Etc.
      • Intermediate value theorem
      • Pinching theorem
      • Rolle's theorem
      • Mean Value Theorem (Rolle's on its side)

Next time: More review; evaluations