Mathematics 133 -- Intensive Calculus

Quiz 9 -- Things to Know

November 15, 2005

The ninth graded quiz of the semester will be given in class on Friday, November 18. There will be two questions similar to problems from the latest problem set and Discussion 7. The first will be similar to one of the questions from Section 4.3 of the text. The other will be a "word problem" where you will need to find a maximum or minimum of some quantity.

Topics to know:

1. The First Derivative Test: If c is a critical point of f and f'(x) is positive for x to the left of c and negative for x to the right of c, then c is a local maximum. Similarly, if f'(x) is negative for x to the left of c and positive for x to the right of c, then c is a local minimum.
2. The Second Derivative Test: If f'(c) = 0 and
   1. f''(c) > 0, then c is a local minimum
   2. f''(c) < 0, then c is a local maximum
   3. f''(c) = 0, then no conclusion is possible
3. How to use these to find local maxima and minima of given functions (built up from the functions we have studied) and solve applied max-min word problems

The quiz questions will be similar to problems from the problem set this week. If you understand those well, you will be prepared for the quiz.