Section 3.7 Worksheet:

Assigned problems: Exercises pp. 190-191, #4, 7, 16, 22, 28, 29, 30, 43 (can you find another plausible solution different from the solution in the back of the book?); 44 (due Tuesday).

1. What is the difference between an explicit equation and an implicit equation?

2. Often implicit differentiation is merely a convenience; it can, however, provide derivatives even when explicit differentiation fails. Find an example on page 188 that illustrates this.

3. How does the strategy for finding the derivative y' change depending on whether an equation is explicit versus implicit?

4. How do we know when two lines are perpendicular (or orthogonal)? What are orthogonal curves?

5. What is the ``folium of Descartes?'' In the equation for the folium, which variable is dependent and which variable independent? What do you notice about the graph of the folium?

Notes:

1. For a ``get out of quiz free'' card, write up a one-page history filled with interesting details about the life of one of
   • Descartes
   • Evariste Galois (p. 188), or
   • Niels Abel (p. 188).
   You can pull good stuff straight off the internet via a search engine (e.g. www.google.com). Be prepared to share with the class!