Semester 2
Click HERE for Semester 1.
Date 
Entry Task 
Activity 
Assignment/Homework* 
2/5 
Download the Course syllabus and save it to your computer's desktop. Scan through each page and take particular note of required materials, assessment procedures, and assignment requirements.  The Hiker and the
Submarine activity. JR: Explain how to use calculus to find where maxima and minima values of a function occur. Include a diagram. 
Read section 3.1; complete pp. 204 #3, 13. 
2/6 
Define
"critical point." Give several (different) examples. 
What Does the Derivative
Say? activity. Work together pp. 206 #68. JR: State the Extreme Value Theorem (see pp. 199) in simple language. 
pp. 205 #21, 31, 35, 45, 53. 
2/7 
Let
f(x) = x^{2}  x  6.
Sketch f(x) on the interval [3, 4].
Compute f(3) and f(4) and note the
behavior of the function between x = 3 and x
= 4.

The
Mean Value Theorem (MVT). Upper and Lower Bounds activity. Being Careful With the Mean Value Theorem activity. JR: Explain the difference between local and absolute extrema. Can f(x) on the interval [a, b] have a local minimum at x = a? Why or why not? Include a diagram. 
pp.
212 #9, 11, 15. 
2/9 
Create a
function, f(x), which is increasing on the
interval (2, 3). What can you say about f '
(x) on the interval (2, 3)? 
Complete screens
1 – 5 of Desmos.

pp. 220 #5, 6. pp. 161 #9. 
2/12 
If f '(x)
= 0 can sometimes be a maximum or minimum value for f,
what do you think f '' (x) = 0 tells us
about f? Explain your reasoning using f(x)
= x^{4} – 4x^{3}. 
Finish the Desmos
activity from Friday, screens 6  20. JR: Explain how to use the second derivative of a function tell you whether a critical value (where f '(c) = 0) is a maximum or minimum. Include a diagram. 
pp. 221 #9, 11, 19. 
2/13 
Under what conditions would "The Second Derivative Test" be inconclusive? Give several different examples.  The Graph Game
activity. Those facing North do Form A; those facing
South side do Form B. JR: Assume f is concave upward. Sketch a graph of f and select an arbitrary point. Draw the tangent to the point. Where is the tangent line relative to f? Will this always be true when f is concave upward? Explain. 
pp.
220 #8, 9. 
2/14 
Work in pairs on the Everything about Extrema sheet.  Work
individually, then check with a table partner pp. 221 #27;
pp. 205 #47. JR: If f '' (a) = 0 what is true about f at x = a? Give several examples, both as functions and graphs. 
Draw a diagram and create a function in one variable
for the following situations:

2/20 
Work in
pairs. Using a standard sheet of paper (8.5" by
11.0") guess the dimensions of opentopped box with the
largest volume that can be made by cutting a "tab" from
each corner of the paper. Build your box.
Compute its volume. 
Write an
equation for the volume of an opentopped box created from
a standard sheet of paper (8.5" by 11.0") if a "tab" is
cut at each corner of the paper x inches
wide. Sketch the flat paper and the box it creates. Optimization Problems. The WasteFree Box activity. JR: Explain a strategy for solving "Optimization Problems." 
pp. 256257 #3,
5, 7. 
2/21 
Define the bold
terms in the section Applications of Business and
Economics (pp. 255256). 
Optimization
Problems. Do pp. 259 #60, 61, 62. JR: When solving an optimization problem, a derivative is taken of a function to determine the location of maxima and minima. Explain at least two ways one can use to verify whether the location is a maximum, minimum, or neither. 
Finish the
problems begun in class. On a standard graphing calculator (e.g. TI84+)
Tmin= 0In the function editor, enter

2/23 
Let a rectangle
have a given perimeter, P. The rectangle has sides L and W
cm long. Prove using calculus a rectangle with the
greatest area is where L = W. 
pp. 257258 #11,
15, 32, 33, 43. JR: What are your strengths and weaknesses with optimization problems? 
Finish the problems begun in class. 
2/26  Assume Safeco
Field holds 40,000 “general” spectators. When the
Mariners charge $35 per ticket, the average attendance for
these seats had been 32,000. When ticket prices were
lowered to $27, the average attendance rose to
36,000. How should ticket prices be set to maximize
revenue? Assume the demand function is linear. 
Questions &
problem demonstrations. JR: Explain why knowledge of "extrema" is important to performing an optimization problem. 
Prepare for
tomorrow's quiz. 
2/27 
Get ready for the quiz! Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people. Place your homework notebook near you for scoring.  Quiz 3.2.
Expect a question on optimization within economics.
Note card OK, no calculator. JR: How well prepared do you feel you were for today's quiz? What did you do to prepare? What else do you wish you would have done to prepare? 
Assume each of
the following functions is the derivative, f ' (x)
of a function f(x). Determine the
"parent function" f(x) for each.

2/28 
If the
derivative of a function results in x^{2},
what was the original function? 
Antiderivatives. Antidifferentiation Formulas activity. JR: Why are "direction fields" (see Figure 1 on page 269 and the Direction Fields activity) an appropriate way to display an antiderivative? 
pp. 273 #3, 13,
19. Review previous homework, quizzes, and tests and bring questions on any concept you are still uncertain. 
3/2 
What conditions
need to be true before applying the Mean Value
Theorem? Give an example of a function that does not
satisfy these conditions. 
Review of MVT:
pp. 212 #10, 13. Review of Limits at Infinity: pp. 235 #9, 10, 17, 23. JR: Explain how to use limits at infinity to determine the horizontal asymptote of a function. Give an example. 
Finish the problems begun in class. 
3/5 
pp. 276278 #1,
6, 9, 11, 16, 29, 33, 40, 47, 53, 55. 
Continue the
review problems. JR: Why is merely performing first and second derivatives of a function insufficient when attempting to determine extrema over an interval? Give an (explicit) example. 
Finish the
review problems through #33. 
3/6 
Create a unique
optimization problem. Make it as authentic as you
can. 
Continue the
review problems. JR: What is a general formula for finding the antiderivative of a power function, e.g. f '(x) = x^{n}? 
Finish the review problems. 
3/7 
Prepare to ask
questions. 
Inclass review. JR: Explain how to determine the shape of a function given a graph of its derivative. Include an example. 
Prepare for the tests. 
3/12 
Get ready for the test! Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people. Place your homework notebook near you for scoring.  Test 3.1: Free
response: you may use one 3 x 5 note card and a
calculator. Expect questions on

Prepare for the next test. 
3/13 
Get ready for the test! Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people. Place your homework notebook near you for scoring.  Test 3.2: Free
response: you may use one 3 x 5 note card and a
calculator. Expect questions on

Bring all your work, including graphs, from Straight Line Kinematics (27 November). 
Date 
Entry Task 
Activity 
Assignment/Homework* 
3/14 
Organize your
charts and data from Straight Line Kinematics.
Explain what you would have to do differently if you used
columns of equal width (one second). 
Areas and
Distances (review Straight Line Kinematics).
JR: Assume you wanted to produce the d vs. t graph from the v vs. t graph from Straight Line Kinematics. Explain the entire process and what you would have to do to produce the most "accurate" graph possible. 
p. 293 #2.
Show all calculations and answer all parts. 
3/16 
Assume you are
given a velocity function for an object and wish to
calculate the object's displacement. Why must we go
through the painstaking steps of a Riemann Sum (adding
areas of columns) rather than merely multiplying velocity
vs. time? 
Explain three
different (but similar) ways to set up a Riemann
Sum. List advantages of each. Two Easy Pieces activity. JR: Under what circumstances will a Riemann Sum with "right endpoints" be larger than one with "left endpoints?" Include diagrams. 
pp. 293294 #3,
16, 19. 
3/19 
Use your
calculator to compute the "area under the curve" for f(x)
= (1 + x^{2})^{1} over the
interval 1 ≤ x ≤ 1. The answer is a real
number but NOT a rational number. What is it in
simplest terms? Why is this? 
Definite
Integrals (this should come after applying Theorem 4). The Area Function activity. If time allows, do the Exploring Definite Integrals activity. JR: Why is the "area under the curve" for sin(x) over 0 ≤ x ≤ 2π the same as x^{3} over 2 ≤ x ≤ 2? Include diagrams. 
p. 307 #23, 33,
34. Copy the graphs. 
3/20 
Compute the sum
of each of the following for the first one hundred Natural
Numbers (i.e. "counting numbers") if the i^{th}
element is a_{i}.

Follow at least
one of the following to learn how to apply Theorem 4 (p.
298)
JR: Explain how the process of expressing an integral is similar to and different from applying the Definition of a Derivative (see p. 107). 
p. 307 #21, 24,
25. 
3/21 
p. 307 #29. 
Review
yesterday's linked resources. View at least
three. Perform the integral in #55 on page 308 using
The Definition of an Integral (Theorem 4 p.
298), completing all steps without notes, assistance, or
calculator. JR: Explain why infinites and infinitesimals are used in calculus. Give at least two examples. 

3/23  Get ready for the quiz! Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people. Place your homework notebook near you for scoring.  Quiz 4.1.
Expect a question asking you to perform an integral using
The Definition of an Integral (Theorem 4 p.
298). No note card or calculator. JR: Explain 

3/26  Let the function f(x) be the integral of x^{2}  x  3. Write the previous sentence in symbolic form then compute f ' (x).  What is Fundamental in the
Fundamental Theorem of Calculus? activity. JR: Why is the Fundamental Theorem of Calculus in two parts? How do these parts differ? How are these two parts similar? 
p. 318 #3, 9, 17, 21. 
3/27 
Let f be
a continuous, differentiable function over [a, b]
where 0 < a < b. Let F
be the definite integral of f using the endpoints
of the interval for limits. Compute F '. 
Indefinite
Integrals and the Net Change Theorem. Clearing The Hill activity. JR: State the Net Change Theorem and explain its application. Include several examples. 
pp. 326327 #5,
9, 11, 21. 
To take the integral of (2x + 1)^(1/2) let u = 2x + 1. Implicitly derive and solve for du. Perform the integration using "u" and your new "du" then substitute back into the answer. This process is called "usubstitution." Why does this work? When does it NOT?  The Substitution
Rule Loki's Dilemma activity. North side do p. 303; South side do p. 304. JR: How is The Chain Rule related to "The substitution Rule?" Give an example. 
pp. 335336 #3, 13, 21, 23.  
See problem #13 on page 339. Explain why "usubstitution" is not necessary to evaluate the integral. Note: the answer is NOT because "u" is used in the problem!  Review
exercises: pp. 338340 #2, 3, 9, 17, 33, 46. Show
all work! Chapter 4 AP AB/BC Review Questions, pg. AP41 (following page 342). Write processes and answers in your homework notebook. Show all work! JR: What role did Eudoxus and Archimedes play in the "invention" of calculus? You may use your computer to find sources of information (remember to reference sources of information you use!!!!!). 
Finish the review and prepare for the tests.  
Prepare to ask
questions. 
Inclass
review. JR: What role did Newton and Leibniz play in the "invention" of calculus? You may use your computer to find sources of information (remember to reference sources of information you use!!!!!). 
Prepare for the tests.  
Prepare to ask questions.  Inclass
review. JR: How is the process of the FTC changed when something other than x is used (such as x^{2})? Give an example. 
Prepare for the tests.  
Get ready for the test! Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people.  Test 4.1.
Free response: you may use one 3 x 5 note card.
Calculators NOT allowed. Expect questions on

Prepare for the
tests. Suggested review problems


/ 
Get ready for the test! Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people.  Test 4.2.
Free response: you may use one 3 x 5 note card and a
calculator. Expect questions on

Given two
functions: f(x) = 4  x^{2}
and g(x) = x. Without using a
calculator, determine where f and g
intersect and the interval for which f(x) ≥
g(x). Compute the area under the curve
for both of the functions over that interval. 
Click here for the Reference Pages from Stewart Calculus (7th Edition).
Create and print your own graph paper at THIS Website.
Below are various documents on the
operation of the class
Also note
the additional items