Fall+Week+15

toc

Monday 11/30
Continuing our study of graph theory, we turned our attention to a couple of problems where the graph of f '(x) is given. Problem 1 was 1985 AB 6. The figure below shows the graph of f ', the derivative of a function f. The domain of the function f is the set of all x in the closed interval [-3,3]. a) For what values of x, -3 < x < 3, does f have a relative maximum? A relative minimum? Justify your answer.

b) For what values of x is the graph of f concave up? Justify your answer.

c) Use the information found in parts a) and b) and the fact that f(-3) = 0 to sketch a possible graph of f.

Solutions:

Problem 2 was 1996 AB 1. The figure below shows the graph of f ', the derivative of function f. The domain of f is the set of all real numbers x such that -3 < x < 5. a) For what values of x does f have a relative maximum ? Why?

b) For what values of x does f have a relative minimum ? Why?

c) on what intervals is the graph of f concave upward? Use f ' to justify your answer.

d) Suppose that f(1) = 0. Draw a sketch that shows the general shape of the graph of the function f on the open interval 0 < x < 2.

Tuesday 12/1.
More work on graph theory but we also began looking at the topic of optimization, or applied max and min. Answers to the AP Problems can be seen in a slide show posted on Thursday of last week. Our introduction to optimization was through one of our favorite(!) problems- the box problem. Following working this problem, we either finished up the AP graphing worksheet or began a set of problems on optimization.

Wednesday 12/2
Review for the test on graph theory was the agenda for the day. We worked on either the AP graph theory worksheet (see Thursday of last week for answers) or the max/min applications worksheet. The answers to these problems are in the pdf file attached below.

Thursday 12/3
Test today.

Friday 12/4
More max/min applications following our problem of the day.