Final Exam Review Sheet
The Standard Caveat:
Any review sheet is a compilation of personal opinions about
the relative importance of various parts of the material. These are jason's. It would be
crazy to rely on any single resource to study for your Exam, including this little study
guide! This time, to make my point, I intentionally left off 3 key concepts. What are
they?
This exam will cover old
material...
•
1.11.7
•
2.12.7
•
3.13.7, 3.9
•
4.14.4
...and new material
•
4.54.6
•
5.15.4
•
6.1,6.2
Yes, indeed, we really
did skip...
•
3.8 and 3.10
•
4.7 and 4.8
The final exam is cumulative. Some of the questions could have been asked on Exam
1 or Exam 2. How many? Most of the questions are designed to test new material, but
a large minority will cover "old" material. This review sheet focuses on the new
sections only because previous review sheets adequately discuss the older ones.
4.5
Speaking of difficult sections! This is the "grown up" version of 4.3. You learned
in 4.3 that a function can be optimized by finding its critical points, checking
endpoints, and using first or secondderivative tests, etc. Now you must apply all of
those skills to problems in which you don't have a simple formula f(x)=x^2+x for the
function involved. You must deduce this formula for yourself, and that requires
geometric intuition. General tips are given on page 198, so I won't repeat. Common
mistakes include:
•
finding critical points, but forgetting to check endpoints, or otherwise verify
that they are the global max or global min sought.
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 Winter '05
 Staff
 Calculus, Derivative, Fundamental Theorem Of Calculus, Riemann

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