Mathematics 133 -- Intensive Calculus

Quiz 6 -- Things to Know

November 1, 2000

The seventh graded quiz of the semester will be given in class on Friday, November 10. There will be one or two questions similar to problems from the latest problem set. One will be a "word problem" where you will need to find a maximum or minimum of some quantity and verify that it is what you want using the First or Second Derivative Test.

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 7th problem set. If you understand those well, you will be prepared for the quiz.