The Final covers all of the material. and the students are responsible for everything I covered in my lectures. Nothing is "unimportant". The later material heavily depends on what we covered in the beginning, so mastering this later material should be your priority.

The Final will consist of perhaps 10 problems that will resemble typical homework problems but you should also know, understand, and be able to correctly state if asked to, the principal theorems of our course:

1. de l'Hôpital's Rule
2. The Intermediate Value Theorem
3. The Extreme Value Theorem
   
4. Fermat's Theorem, Rolle's Theorem, The Mean Value Theorem
5. The Fundamental Theorem of Calculus
6. The Mean Value Theorem -- Integral Version (5.3)

The following list of topics should be helpful in your preparations:

• Chain Rule (2.5)
• implicit differentiation (2.6)
• related rates (2.7)
• derivatives and the shape of graphs (what does f´ and f´´ say about f, 4.3)
• exponential and logarithm functions (3.1-3.3)
• exponential growth (3.4)
• inverse trigonometric functions (3.5)
• hyperbolic and functions (3.6)
• curve sketching (4.4)
• optimization problems (4.5)
• Newton's Method (4.6)
• The Substitution Rule (boxed formulae 4 and 6 in Section 5.5 -- ignore Stewart's mention of differentials in the Substitution Rule)
• Applications of Integration (7.1-7.3)