# MCS 118, Fall 2016 ### Course information

• Course information/ Syllabus
• Instructor's contact info and schedule

• ### Tentative schedule and deadlines

DateIn-Class Daily HW to complete before class (highly recommended but I will not collect them) Problems (graded)
1. Tues, 6 Sept Setting the Stage ---
2. Thu, 8 Sept
• Velocity and distance traveled
• Evaluating functions
• Evaluating a difference quotient (compare to textbook Example 8, p73)
• exercises from 1.1: page 74: #7,9 (see reading to see the point of these).
• Skills 1 or Skills 1 version b (Due Thurs, 8 Sept)
Skills 1 Solutions [PDF]. Brush up on the parts that you didn't get full credit for:
• Expand a product or power: Khan Academy
• Factor out greatest common factor: Khan Academy
• Simplify by factoring and cancelling: Khan Academy (really nice lesson)
• 3. Fri, 9 Sept
• New definitions (not from text): The net change in a function f over an interval [a,b], and the average rate of change in f over [a,b].
• Examples of interpreting net change and average rate of change.

• Read: 1.1 pages 70-73. Understand the definition of the word "domain" from the textbook.
• Read: 1.2 pages 79-82. Analyze how the words "increasing" and "decreasing" are used.
• exercise from 1.1: work through Example 8.
• other exercises from 1.1: page 75: #29-35 (odd numbers only); 43, 49, 53; page 76: #83,85,87. Check answers on the back of the book.
• 4. Mon, 12 Sept
• Review from reading (sec 1.2):
• Zeros: where they live, finding them on a graph, using algebra to solve for them from a formula.
• Increasing and Decreasing Intervals: definitions, and what these intervals look like on a graph (but no way to find or solve for them algebraically yet).
• Reasoning group worksheet: on increasing and decreasing [PDF]
• 3 graph examples [PDF]
• Read: 1.2 pages 79-83 (for the second time).
• Study Example 3 in sec 1.2 (finding zeros, pg 81)
• Study the definitions of "increasing" and "decreasing" in sec 1.2 (pg 82).
• Study Example 4 in sec 1.2 (increasing and decreasing function, pg 82).
• Finally, attempt these exercises from 1.2 (page 87): #17, 21; #31, 33, and #40 (use desmos.com, or another graphing software like your graphing calculator).
• If you have trouble with these exercises, please email me with questions before class on Monday)
• 5. Tues, 13 Sept
• Discussion of the Increase and Decrease worksheet.
• Review linear functions. Note: In this class, we define linear functions (algebraically) to be functions having the type of formula `g(t)=mt + b`.
• Defn of turning points: values in the domain where a function changes from increasing to decreasing or vice versa.
• Finish the worksheet on increasing and decreasing at home. Be prepared to discuss this in class on Tuesday (and it's OK if your group's answers are not quite correct).
• Read: P.1 pages 2-6 (solving equations algebraically)
• book exercises from P.1 (page 11): #13, 19, 45, 55, 57, and 101.
• book exercises from 1.2 (page 87): #17, 21, 31a, 33a, and 41a.
• 6. Thurs, 15 Sept Review:
• Slope of a line through two points,
• using "point-slope form" to write an equation for a line through a known point with a known slope.
• Read: 1.2 page 84 (linear functions). See Examples 6 and 7.
• Skills 2 and Skills 2 answer key [PDF] (Due Thurs, Sept 15, beginning of class). Resources: see P.1 (pages 2-8) for review of solving equations and see P.5 for a review of computing slope and writing equations of lines.
• Online review, and extra practice:
• 7. Fri, 16 Sept
• A secant line is the line through the two points (a,f(a)) and (b,f(b)) which lie on the graph.
• Some of you observed that the slope of the secant line is equal to the average rate of change in `f` over the interval `[a,b].`
• Linear function and motion Group worksheet. Check solution.
• Read: review P.5 pages 47-52. Work through examples.
• Book exercises from P.5: pages 56 #25, 33-34, 35-38.
• Book exercises from 1.2: pages 87 #19, 59, 69, 71.
• Watch Khan academy: computing secant line.
• On your own notebook, write a linear function which does not cross the origin. Sketch an accurate graph of this function, with 4 points of the graph labeled. Check with Desmos.com or another graphing tool. I will grade this during class.
• Be ready to discuss this question: If `f` is a linear function, why should `f` have the same average rate of change over every interval `[a,b]` ?
• 8. Mon, 19 Sept From Sect 2.1-2.2:
• polynomial function (Sec 2.1 p136).
• The degree of a polynomial and the leading term of a polynomial.
• Monomials: polynomials with just one term (Sec 2.2 p148).
• The shapes of graphs for basic power functions: even-degree power functions vs. odd-degree.
• The Leading Coefficient Test (Sec 2.2 p149) - determine the end behavior of a polynomial (by examining its leading term).
• Problem Set 1 (Due Mon, Sept 19, beginning of class).
• Problem Set 1 Solution
• 9. Tues, 20 Sept Sec 2.2-2.3.
• Basic properties of polynomial functions and their graphs (p147).
• Degree of a polynomial, the maximum number of zeros, and the maximum number of turning points.
• The connection between zeros of a polynomial and factors of the polynomial.
• Using polynomial division to factor a polynomial when one of its zeros is know.
• Sec 2.1 p136-137
• Sec 2.2 p147-150. Work through the examples.
• Exercises:
• Sec 2.1 (p142) #1-8 (without using technology);
• Sec 2.2 (p154) #13-19 (do by hand, then check using graphing technology) and #23-26 (do use graphing technology like Desmos.com for these).
• Sec 2.2 p147-153 (work through Examples 5 and 6).
• Sec 2.3 p158-159 (for examples of long division of polynomials).

• Exercises:
• Sec 2.2 (p154) #1 (Use end behavior, roots, and turning points to match them without using a calculator), #27-37 (odd), #91-93.
• Do the examples of division given in §2.3.
• Take-home quiz 1 and Solution for quiz 1 (Due Thurs, 22 Sept at the beginning of class)
Syllabus Quiz (Problem 0)
(Due date moved to: Thursday, 22 Sept, during office hours - my door is usually open during the week, and you can also make an appointment by email.)
Fri, 23 Sept Shorter class period today! At 12:45-1:20pm.
• In-class (NEW) Review for Test 1 and Solution of Review for Test 1
• (OLD) Rough draft PREP for Test 1
• Mon, 26 Sept TEST 1 (during class). No notes or calculator. Test 1 Solution
Tues, 27 Sept Nobel conference (no class)
Thurs, 29 Sept
• Sign Behavior near a zero of a function.
• Sec 3.2: The idea of a limit and reading limits from graphs.
• In-class exercise: Limits and function values and Solution
• Fri, 30 Sept Recap: reading limits graphically. Estimating limits from a table of values. Theorems: some basic functions and their limits. Read:
• Sec 2.2 p151 about repeated zeros and multiplicity,
• p152 Example 5 (again, if you have already been through it once).
• Sec 3.2 p210-212 (work through Examples 1 and 2; attempt the Exploration on p210)
Textbook exercises: Sec 3.2: #1-12 (odd), #37 and #38 (discuss with a classmate afterwards, if possible)
• Algebra Skills 3 (your answers will be checked, but you will get full credit for turning this in) (due Friday, 30 Sept)
Solution to Skills 3
Mon, 3 Oct Sec 3.3 Evaluate limits directly from the formula from a function, without referring to a graph or table of values.
• Fact: All limits of polynomial functions can be evaluated by direct substitution
• Tues, 4 Oct Sec 3.3 Facts:
• Limits of rational functions can also be evaluated by direct substitution as long as it doesn't lead to division by zero;
• simplifying by factoring and canceling can help evaluate limits of rational functions in cases where the denominator is going to zero.

• Sec 3.4: Def of continuity.
• Sec 3.3 pp218-222, but ignore the "proof" under Thm 3.1 on p218.
• Work through Examples 1, 2, 3, 5, 6

• Textbook exercises: Sec 3.3 p224 #7,9,11,13,15, 39, 41.
Problem Set 2 and Problem Set 2 Solution [PDF](due Tues, Oct 4)
Thurs, 6 Oct Sec 3.4:
• new vocab terms removable vs non-removable discontinuity
• new concept and notation: One-sided limits: limit as x->c from the left, limit as x->c from the right.
• Connecting one-sided and two-sided limits (Theorem 3.8 p230).
• Skills 4(due Thurs, Oct 6) with Skills 4 Answer Key [PDF]
1. IXL: Add and subtract rational expressions
2. Khan Academy: Nested Fractions (Do the practice questions)
Fri, 7 Oct Sec 3.4: one- and two-sided limits, continuity, removable and non-removable discontinuities.
• Worksheet: limits and continuity
• Recall facts about continuity (Thm 3.3): Continuity of polynomials ("polynomials are continuous everywhere!") and continuity of rational functions ("rational functions are continuous everywhere they are defined").
• Re-read Sec 3.3 Theorem 3.3 (p219) and Examples 3,6, and 6.
• Sec 3.4 p227-230 up to (and including) Example 4.
Textbook Exercises: Sec 3.4 #1-6, #31,33,35 (optional: you can use graphing technology)
• Take-home Quiz 2 (due Fri, Oct 7). You may ask me for help. Quiz 2 Answer Key [PDF]
Mon, 10 Oct Intermediate Value Theorem (IVT): Thm 3.11, p233 (Sec 3.4)
• 10 True/False questions [Plain text]

• Short intro to Sec 3.5 Infinite Limits - how to describe the behavior of a function when its output values get large and positive or large and negative.
Suggested exercises:
• do earlier suggested exercises above from Chapter 3.
• Review p227-231, including the examples.
• Do #23-26. For each: Identify interval on which the function is continuous; identify any points at which the function is discontinuous, and classify each discontinuity as removable or nonremovable.
• Nothing to submit
Tues, 11 Oct
• Sec 3.5 Infinite Limits - how to describe the behavior of a function when its output values get large and positive or large and negative.
• Limits of square roots (p220).
• Algebraic technique: multiplying by a conjugate to simplify fractions involving square roots.
• Short intro to Sec 4.1: from tangent line to derivative
• Sec 3.4 p233-234 (I'll ask you to state the Intermediate Value Theorem on Test 2)
• Sec 3.5 p238-241 (infinite limits). Go through Examples 1-4.

• Textbook exercises:
• Sec 3.4 #67 and 68 (do without graphing! Use the IVT in your explanation), #78 and #79.
• Sec 3.5 #1,2,3,5,29,30,31 (For now, use a graphing technology to examine the graphs of these functions, and read your answer from the graph).
• Take-home Quiz 3 (due Tues, Oct 11 at the beginning of class).
• Quiz 3 Answer Key [PDF}
• You may make an appointment to ask me for help!
• If you missed class (for any reason), you can email me for a copy of the quiz (there is no penalty for emailing me asking for a copy of the quiz).
• Thurs, 13 Oct
• New: computing infinite limits analytically.
• Limits of rational functions when the denominator goes to zero, but the numerator goes to a nonzero value: the function will go to +Infinity or -Infinity, but you have to analyze the signs of all the factors in the fraction carefully to decide which.
• Worksheet: infinite limits and signs (Solution)
• Try exercises: Sec 3.3 (p225) #17,19, 21; 42, 43, 44.
• Read: Writing Tips for Limits
• Skills 4B and Skills 4B Answer Key (due Thurs, Oct 13)
Fri, 14 oct Further examples, and time to continue working on the Worksheet: infinite limits and signs (Solution)
• Read: Sec 3.5 p239-242 (Example #5 goes a little beyond what we've seen in class so far, but you should be able to understand it).
• Textbook Exercises: Sec 3.5 #7,8 (using the graphs that are provided); #9,11,13 (without graphing); #29-35 (odd ones first, then try the even-numbered ones for more practice).
• Finish in-class worksheet: infinite limits and signs
• Read: Writing Tips for Limits
• Problem Set 3 and Problem Set 3 Solution (Due Friday, Oct 14)
• Mon, 17 Oct Review for Test 2: Review worksheet and Solution
• Chapter 3 Review (p246) #11, 13, 15, 39, 47, 49, 51, 53, 55.
• Study for Test 2: do suggested exercises from Sec 2.2, 3.2-3.5.
• Nothing to submit
Tues, 18 Oct TEST 2 and Test 2 solution Nothing to submit
Thurs, 20 Oct Computing the slope of a tangent line nothing to submit
Fri, 21 Oct Sec 3.1: The derivative of a function: a related function which gives slopes of tangent lines. Examples and exercises.
• In-class worksheet derivatives and Answer key
• nothing to submit
(24-25 Oct Fall Break)
Thurs, 27 Oct Sec 4.1
• Review: definition of the derivative.
• Terminology: What it means for a function to be differentiable at a point, and differentiable on an interval.
• Graphical properties of differentiable functions, and typical behaviors at points where a function is not differentiable (4 examples).
• Theorem 4.1: Differentiability implies continuity.
• Read Sec 4.1 p252-257 (up to and including Example 5).
• Book Exercises:
• Work through the examples in the reading above, carefully.
• Attempt Sec 4.1 (p259) #1,2,3,4,7,17,18, 25.
• Fri, 28 Oct
• Sec 4.1. Matching properties of the graph of f(x) with the graph of its derivative f'(x).
• Neat fact: Using the derivative to find the turning points of a polynomial function.
• In-class exercise: Points of interest and Solution
• Re-read all of Sec 4.1 p252-259, including reworking Examples 1-5.
• Copy out the statement of Theorem 4.1 from the text. Allow some time to pass and rewrite it from memory. Compare to the correct statement in the text. Book Exercises: Sec 4.1 #71-80; #87, 88, and 90
• Problem Set 4 with Solutions due date was extended to Fri, Oct 28
Monday, 31 Oct Sec 4.2
• Notation: "d" notation for derivatives.
• Derivatives of constant functions and linear functions.
• Derivatives of power functions.
• The expansion of binomials.
• The power rule for differentiation.
• Handout:Expanding Powers of Binomials [PDF]
• Book Exercises: Sec4.1 #14, 18, 28 (ignore part c); #35-38, 39, and 40; 49. Skills 5 with Answer key (due Monday, Oct 31)
Tues, 1 Nov Sec 4.2. Derivatives and sums, differences, and constant multiples. Differentiating all polynomials. Rewriting roots and fractions as power functions. Read:
• Sec 4.2 p263-266.
• work through examples 2, 3, and 4.
• Quiz 4 with Answer key(due Tues, Nov 1). Email me for a copy of the quiz if you missed class.
Thurs, 3 Nov Sec 4.3 Derivatives of functions built up by multiplication (products)
• Read Sec 4.2 p266-269, work through examples 5-9 carefully.
• Textbook Exercises: Sec 4.2 #3-19 (odd; evens if you want more practice), 33-36, 45, 47, 49
• Nothing to submit
Fri, 4 Nov
• Geometrical explanation (via area of rectangles) of the product rule.
• Quotient rule (without explanation)
• Second, third derivatives, etc.
• Read all of Sec 4.3 (lightly read the proof of the product rule).
• After reading Examples 1-4, rework them yourself.
• Book Exercises: Sec 4.3 #1-9 (odds; evens for more practice), 13, 15, 21, 23 (refer back to p278 for similar examples), 47, 51, 53, 63, 65, 75-78, 89.
• Problem Set 5 (due Fri, Nov 4) and Problem Set 5 Solutions
Mon, 7 Nov Sec 5.2:
• Rolle's Theorem (Thm 5.3, p322). Illustration and interpretation: in graphical terms (horizontal tangent lines) and motion terms (times with zero instantaneous velocity).
• Mean Value Theorem (Thm 5.4 p324). Statement of the theorem, illustration, and interpretations.
• Also, notation for higher order derivatives (sec 4.3) at the end
• Finish the exercises from Sec 4.3 listed on above
• Sec 4.3 #67, 69, 71
• Chapter 4 Review (p308) #37,41, 45, 46
• Skills 6 and Skills 6 Answer Key (due Mon, Nov 7)
Tue, 8 Nov
• How the general case of the Mean Value Theorem can be deduced from the special case of Rolle's Theorem (which is intuitively easier to understand).
• Handout: Rolle's Theorem to MVT and Solution to Handout
• Read Sec 5.2 p322-325. Read lightly through the proofs for now to get the idea.
• Continue the suggested textbook exercises from previous two days that you have not finished yet.
• Quiz 5 (due Tues, Nov 8) and Quiz 5 Solution. Email me if you need a copy of the quiz. The suggested reading (Sec 5.2 p322-325) will help you with #3 on the quiz.
Thurs, 10 Nov Short 2-page practice questions for Test 3 Complete Prep for Test 3 and Solutions to Complete Prep for Test 3. Fyi, computational answers could be checked using wolframalpha.com
Fri, 11 Nov Test 3 and Test 3 Solutions. Topics: lecture days Oct 20 – Nov 8: book Secs. 4.1, 4.2, 4.3 on derivatives, and Sec 5.2 on Rolle’s Thm and MVT.
Mon, 14 Nov
• Composition of two functions: The output of one function is used as input for another one.
• Notation for composition of functions.
• Chain Rules: Expressing the derivative of a composition in terms of the two pieces.
• Nothing to submit
Tues, 15 Nov Sec 4.4
• Worksheet: Composition and Derivatives and Solution.
• Applying chain rule to differentiate composite functions;
• Recognizing that a particular function is a composition of two functions;
• Generalized Power Rule (Thm 4.9, p286)
• Read Sec 1.4 (composition) p103-105 (work through examples)
• Read Sec 4.4 (chain rule) p284-286. Work through Examples 1-3.
• Book exercises: Sec 1.4 p107 #39,41,43,45,51,53,55,57, and #62,63.
• Nothing to submit
Thurs, 17 Nov Different ways of expressing the chain rule, and using the chain rule in combination with other derivative rules. Intro to Sec 4.5: horizontal and vertical tangent lines to a circle.
• Read all of Sec 4.4, p284-289. Work through Examples 2-6 (chain rule). Work through Examples 6-9 (how to simplify after differentiation in a clear, readable way).
• Book Exercises: Sec 4.4 #1-12 (odd numbers first); 47, 59, 60, 61.
• Nothing to submit. I will give you take-home quiz 6 (email me if you are out)
Fri, 18 Nov
• Sec 4.5 - Implicit Differentiation. Using the Chain Rule to compute slopes for graphs and curves when you can't isolate y as a function of x. e.g. tangent lines to ellipses.
• Intro to of Sec 4.6 Related rates: e.g. area and radius of a growing circle are related by a mathematical formula (such as A = πr^2), so their rates of change must also be related.
• Read Sec 4.5 p292-296 for many patiently-worked out implicit diff examples; you'll need to work through them yourself to get fluent with the process.
• Book Exercises: After you do the reading and work the examples in the section, try Sec 4.5 p297 #1,4, 5, 15, 21.
• Take-home Quiz 6 (due Fri, Nov 18). If you will be out for field trips or other reasons, you can email me for the quiz problems and to give me the solutions.
• (Optional) One-sided index card 'cheat sheet' (written in easy-to-read-sized font) for Optional Cumulative Test due on Friday, 18 Nov. Index cards will be handed out on Thursday. Suggestions: include the quotient rule, definition of derivative, IVT, MVT, but not much more. It will slow you down if you include too much.
• Mon, 21 Nov Sec 4.6. Relation between A and r in a circle (see Ex. 2, p301). Ex: A growing sandpile (see #23, p305).
• Read Sec 4.6 p300-302. Read the exposition and work through Examples #1-3.
• Book Exercises: Sec 4.5 #25-31 (odd), 33a, 47; Sec 4.6 #15 (Hint: see Example 2 in the section).
• Problem Set 6 (due Mon, Nov 21)
Tues, 22 Nov (Optional) Cumulative Test and Solution to Cumulative Test. Topics: Mostly materials from Test 1, 2, 3, plus a couple questions from materials taught during lecture days Nov 14-18.
To prepare for this test:
• Do ALL suggested HW from Nov 15-21.
• Do the prep questions created for Test 1, Test 2, Test 3.
• Read book Sec 4.6 Ex. 4 (p301).
Thanksgiving
Mon, 28 Nov Sec 5.1 The Extreme Value Theorem, critical numbers, and extrema on a closed interval.
• Rework Examples 1-5 (p300-303) on your own (solve it without looking at the book, and then compare to the textbook solution).
• Then try Sec 4.6 #3, 4, 15, 16, 17-24, 27, 28, 32, 33, 38. Or, you pick and choose problems that look interesting to you from among the physical problems from #17 on. Any formulas from geometry, you can look up inside the front cover of your textbook, from Wikipedia.
• Tues, 29 Nov
• Review of "critical numbers" and finding maxes and mins on closed intervals (Sec 5.1 p317-318).
• Sec 5.3:
• Thm 5.5 (p329): How the sign of the derivative `f'(x)` describes the increasing/decreasing behavior of the function f(x), that is, how to algebraically determine the intervals on which practically any function is increasing and decreasing.
• Thm 5.6 (p331): the changes from increasing to decreasing or decreasing to increasing are the places where maxes and mins occur!
• Read Sec 5.1 p314-318. Work through Ex. 2 and 3 on p317-318 (meaning, after you have read through them, copy the problem out and rework it on your own to see if you've really understood and remembered the process).
• Book Exercises: Sec 5.1 (p319) #1-13 - it's not a lot; most of these are answered just by looking at a graph, without any calculating. But you'll need to understand the terms and definitions from the reading!
• Routine Skills 7 (extended to Thurs, Dec 1). This is graded based on effort, as usual. Check your solution with technology such as WolframAlpha.
Thurs, 1 Dec More on the important Thm 5.5 and 5.6 from Sec 5.3. In-class exercises (practice for Quiz 7): Increase/Decreate/Max/Min with Solutions
• Read: Sec 5.1 p317-318 (if you have not).
• Memorize statements of Theorems 5.5 and 5.6.
• Work through Examples 1-4 as described above (read, understand, copy the problem, and rework on your own)
• Book Exercises: Sec 5.1 p319 #14,16, 17, 19, 21, 45, 46, 47-50 (many of these are graphical exercises that don't require a lot of calculation); Sec 5.3 p335 #1,3,8,11,15,17,19
• Skills 7b is due Thurs, Dec 1. Skills 7b Solution. To answer the question regarding relative max and min, read Theorem 5.6.
Fri, 2 Dec
• IN-CLASS individual quiz and team quiz: A one-sided index card is allowed. The materials are from Sec 5.1 and 5.3. Memorize Thm 5.1, definition of critical number, Thm 5.2, Thm 5.5, Thm 5.6 from Sec 5.1 and 5.3.
• New concept: concave up and concave down on an interval.
• Read the in-class worksheet and the solutions. Review Sec 5.3 in the textbook once more. Continue with unfinished exercises from Sec 5.1 and 5.3 (suggested above).
Mon, 5 Dec
• Concave up and concave down on an interval. Defns (p338) and graphical interpretations (see Fig 5.23 p338).
• Thm 5.7, p339: Intervals of concavity can be determined by studying the second derivative.
• Defn of inflection points (p 340-341)
• Read Sec 5.4 p338-341. Work the examples and study the figures that go along with them!
• Book Exercises: Sec 5.4 #1,2,3 (solve these analytically using the second derivative, but look at the graph that's provided to see if your answer matches), #9, 11, 13, 15, 37 and 38, 65.
• Turn in your one-sided note card for Test 4.
Tues, 6 Dec
• Test 4 and Test 4 Answer Key
• Prep Test 4 and Solution to Prep Test 4.
• Short Prep Test 4 (see solution on regular-length Prep Test 4)
• Review quizzes, in-class worksheets, skills, problem sets, and suggested textbook exercises starting from lecture day November 14 (that is, starting from Sec 4.4).
• Thurs, 8 Dec
• Intro to optimization: Putting the "extreme values on closed intervals" theory to work.
• Team worksheet: optimize! and Answer Key to Team worksheet: optimize!
• Do textbook exercises to prepare for Quiz 8 (see the list of exercises below)
Fri, 9 Dec
• In-class Quiz 8 from Section 5.7 (figuring out maximum profits, etc). and Team Quiz 8 solution
• Individual Quiz 8 and Individual Quiz 8 solution The questions will be like Examples 1, 2, & 3. To prepare, read:
• all of Examples 1-5, p364-368.
• textbook exercises (Sec 5.7 p369-371):
• #7 (maximum product)
• #11 (minimum perimeter)
• #19 (minimum fencing for a pasture)
• #21 (max volume),
• #23 (max area),
• #29 (least amount of paper),
• #43 (minimum area),
• #51 (maximum profit),
• #53 (the point of diminishing returns)
• Closed-book, but you are allowed to bring one-sided small index card. You do not need to memorize or write down formulas for volume/area of object other than a rectangle/box. Each team can use one calculator.
• In-class Quiz 8 (individual and with team) on Fri, Dec 9
Mon, 12 Dec
• (Sec 5.7) Real-life applications (even if they are idealized compared to real-real life): Modeling quantities to be maximized and minimized. In-class example: optimizing a soda can for minimal surface area, given a desired volume.
• Work on Problem Set 7 during class.
• Read Review Sec 5.7 p364-366. Work through Examples 1-3 carefully.
• Book Exercises: Sec 5.7 #21, 22, 23 (you may need to look up some formulas for area of perimeter), and 24.
• Further Reading: Read exercises Sec 5.7 #45, 46, 48, 49, 50, 51 for more ideas about applications where calculus can be used to optimize.
• Tues, 13 Dec Work on Problem Set 7 during class.
New: Knowing the derivative of a function `f`, can you guess the function `f`?
• Problem Set 7 (4 pages): Part I and Part II, due Tues, Dec 13 at 4pm.
• Problem Set 7 Answer Key
• (Wed, Dec 14 is the last day of classes) Class/review session in the usual classroom or my office at 2-3pm.
Thurs, Dec 15 Gustavus College Reading Day
Sat, Dec 17 FINAL EXAM at 8-10am, location OHS 220 (in the 2nd floor Olin, but NOT the usual classroom) Studying recommendation for the final exam