Calc 1A

Assignment Four

We now know what a derivative is and various techniques for finding them. With this behind us, we can now apply our knowledge in various settings. We will begin by working on problems known as "related rates" problems. There are times when 2 variables are related and both are dependent on some third variable, for example, time. Then it would seem reasonable that the rates at which these variable change with respect to time should be related as well. In fact they are, and the relationship between the rates of change of the two variables is dependent on how the two variables were initially related. In any event, these sorts of problems are among the most standard of applications of derivatives. We will explore the second derivative (f'') now in terms of its usefulness in measuring rates of change of a derivative function (f'), and as a device for determining the concavity of the graph of the parent function (f) over intervals. We will define terms related to the study of extrema and use both the first and second derivative to determine whether a critical value of f yields a maximum, a minimum or a stationary point. After that, we will then apply the study of extrema to 'real life' problems, often referred to as "applied max/min problems" or sometimes "optimization problems". These problems arise when one wishes to maximize or minimize a quantity but is subject to various constraints. Finally, we will look at simple problems of rectilinear motion. We will talk about the relationship between position, velocity and acceleration and how these quantities relate to derivatives. Later in the year, we will revisit these concepts once we have learned about integration.

Day Number	Class Topic	Homework-Reading Class notes and Examples is part of EVERY NIGHT'S homework.
One	Related Rates- Basic problems including right triangles.	Pg 274 # 1,5,9,11,13
Two	Related Rates-more examples, including similar triangles.	Pg 274 # 3,15,17,21, 23, 29  (draw an aerial view), Pg 260 #5,13,21,35
Three	Practive with Related Rates	COLLECTABLE HW DUE pg 274# 24,26,38
Four	First andSecond Derivative: Increase/Decrease,Concavity and Inflection	Pg 274 #25,27 Pg 296 #1, 3, 5, 7,19, 25
Five	More with second derivatives. Fun with graphs.	Pg 296 #15,31,33,39,43,53 Pg 274 #33 Pg 319 #23
Six	Extrema: Local/Global Extrema, using 1st and 2nd derivative test, Extreme Value Theorem?	Pg 304 #1,3,5,7,11,15
Seven	Quiz on Days 1-5 Extreme Value Theorem, use of end behavior to determine global extrema if they exist.	Pg 337 #1,3,5,9,11,25,35 Pg 304 #13,43,47
Eight	Applied Max/Min: Simple set ups, strategies, fence problems	Pg 348 #1,3,5,11 Pg 337 #7,13
Nine	More Max/Min : Inscribed Shapes, Box, cutouts	Pg 348 #9,13,15,17,19,23
Ten	Practice with Max/Min	SUPPLEMENTAL MATERIALS
Eleven	Long Quiz: and other things	Christmas break
Twelve	Rectilinear Motion	Pg 359 # 1,3,5,11,13,15
Thirteen	Mean Value Theorem