## Mathematics 101## Calculus I |

*Chapter 4: Applications of Differentiation*

- 4.1 Related Rates (pdf)
- 4.2 Maximum and Minimum Values (pdf)
- 4.3 Derivatives and the Shapes of Curves (pdf)
- 4.4 Graphing with Calculus and Computers (pdf)
- 4.5 Indeterminate Forms and l'Hospital's Rule (pdf)
- Biography and portrait of Guillaume Francois Antoine Marquis de l'Hospital (1661-1704)
- Wikipedia entries for Guillaume Francois Antoine Marquis de L'Hospital (1826-1866) and for l'Hospital's rule.

- 4.6 Optimization Problems (pdf)
- 4.7 Applications to Economics (pdf)
- 4.8 Newton's Method (pdf)
- 4.9 Antiderivatives (pdf)

- 4.1 -- 1, 2, 4, 8, 10 (ships), 11 (plane), 12 (shadow), 14 (spotlight), 15 (walking), 17 (triangle), 18 (boat), 20 (particle), 26 (kite)
- 4.2 -- 2, 3, 6, 9, 21, 27, 39, 43, 55 (density of water), 57 (food-price index), 58 (space shuttle), 59 (trachea)
- 4.3 -- 1, 3, 4, 5, 6, 12, 23, 35, 39, 46 (Coulomb's Law), 47 (VCR's), 48 (bell-shaped curves)
- 4.4 -- 6, 9, 11 (asymptotes and intercepts), 15 (CAS), 20 (parametric curve)
- 4.5 -- 5, 11, 17, 25, 29, 32, 41, 47, 49 (l'Hospital's Rule), 51 (CAS), 60 (cable insulation)
- 4.6 -- 3, 5, 7 (fence), 8 (box), 16 (rectangle), 28 (swimming fish), 29 (beehive), 30 (boat), 32 (lake)
- 4.7 -- 1, 2, 3 (cost), 4 (revenue), 7, 9 (profit), 14 (airplane), 15 (baseball)
- 4.8 -- 1, 4, 8, 14 (roots), 23 (bad initial approximation), 25 (Newton's method fails), 26 (max)
- 4.9 -- 7, 13, 15, 25, 29 (antiderivative), 31 (sketch), 33 (direction field), 40 (particle), 41 (stone), 44 (two balls), 48 (braking), 54 (rain drop)

Use the following exercises to review and test your understanding of the material in Chapter 4. This is not homework, and there is nothing to hand in from this activity.

- Review Exercises, Chapter 4, pp. 336--338 -- 2, 5, 18 (CAS), 27, 33 (shadow), 35 (balloon), 43 (velocity of a wave), 46 (profit), 48 (Newton's method), 51 (antiderivative)

The following Mathematica notebooks are available in two formats. Download the Mathematica notebooks (nb) to your machine and use Mathematica to interpret their contents, or click on the web page link (html) to see a static image of the evaluated notebook.

- 4.2 Maximum and Minimum Values nb html
- 4.3 Derivatives and the Shapes of Curves nb html
- 4.4 Graphing with Calculus and Calculators nb html
- 4.7 Newton's Method nb html