Mathematics 133 -- Intensive Calculus
Quiz 8 -- Things to Know
November 15, 2000
The eighth graded quiz of the semester will be given
in class on Friday, November 17. There will be 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 possibly verify that it is
what you want using the First or Second Derivative Test. The other
will be similar to one of the questions from Section 3.1 of the
text and Discussion 7.
Topics to know:
- 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.
- The Second Derivative Test: If f'(c) = 0 and
- f''(c) > 0, then c is a local minimum
- f''(c) < 0, then c is a local maximum
- f''(c) = 0, then no conclusion is possible
- 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
- Estimating the total distance traveled given a table of
values for a velocity function (see section 3.1 and Discussion 7)
The quiz questions will be similar to problems from the
8th problem set. If you understand those well, you will
be prepared for the quiz.