Period 7 BC Calculus Sunday 19/10/2008[2.3.5.7.8] day 2

Warm up – 10 minutes

• Sample AP Free Response – differentiation rules• Surprise, surprise; this is like an exam question, so pay attention

Implicit differentiation - 20 minutes

• First, this is not on the differentiation rules exam• What happens when you can’t express f(x)?• How do we find the derivative of an inverse?

Quiz – applied rates and trigonometric derivatives – 30 minutes

• Part II of Chain rule homework

Homework

• Exam – differentiation rules – day 5• Note: mastery of the rules is expected. You should prepare to achieve 100% on the upcoming exam

Announcements

Period 7 BC Calculus Monday 20/10/2008[2.3.5.7.8] day 3

Warm up – 10 minutes

• Practice implicit differentiation

Implicit differentiation [cont] - 20 minutes

• X as a function of y• Equation of tangent lines• Inverse trig• Orthogonal trajectories

Higher Derivatives – 25 minutes

• Graphs• Higher implicit derivatives• Formulas

Review quiz – 10 minutes

• Study for exam• Homework for implicit and higher derivatives will be given after the exam

Homework

• Exam – differentiation rules – day 5• Note: mastery of the rules is expected. You should prepare to achieve 100% on the upcoming exam

Announcements

Period 7 BC Calculus Wednesday 22/10/2008[2.3.5.7.8] day 5

Warm up – 10 minutes

• What is the AP Calculus BC exam?• What is the format of the exam?• What do I have to learn?• What is Mr. Carreon going to teach me?

Exam – differentiation rules – 45 minutes

• 2.5 #7, 11, 24, 37, 45, 49, 59, 65• Handout 3.7 #16, 18, 20, 23, 27, 42, 47, 59

Homework

Announcements

Period 7 BC Calculus Sunday 26/10/2008[2.3.5.7.8] day 7

Warm up – 10 minutes

• Exam review/correct/discuss

Derivatives of exponential and logarithmic functions

• Derivative of logs from implicit differentiation• Chain rule with e and ln• Logarithmic differentiation• e as a limit

Homework

• See handout – this will be due day 2, but you’ll have other hw.

Announcements

• Quiz – derivatives of exp and log functions – day 2• Exam – applications of the derivative I – day 5

Period 7 BC Calculus Monday 27/10/2008[2.3.5.7.8] day 8

Warm up – 10 minutes

• Page 148 #77

Linear approximations and differentials – 35 minutes

• Approximating function values• Applications (First-degree Taylor polynomials)• The differential• Relative error

Introduce lab project – Taylor polynomials – 5 minutes

• 3.9 #15, 17, 23, 27, 33, 43, 45, 49, 52• Q & A day 3

Homework Q&A – 15 minutes

• Quiz – derivatives of exp and log functions – day 2• Exam – applications of the derivative I – day 5

Homework

Announcements

Period 7 BC Calculus Wednesday 29/10/2008[2.3.5.7.8] day 2

Warm up – 15 minutes

• Begin Taylor Polynomial Lab

Introduction to related rates – 25 minutes

• Everything changes with time• Triangles• Rectangular areas• Conical piles

Quiz – derivatives of exp and log functions – 30 minutes

• 2.6 #3, 7, 13, 15, 18 - 23

Homework

• Exam – applications of the derivative I –day 5

Announcements

Period 7 BC Calculus Sunday 2/11/2008[2.3.5.7.8] day 3

Warm up – 15 minutes

• Continue Taylor Polynomial Lab

Related rates – 50 minutes

• Everything changes with time• Triangles• Rectangular areas• Conical piles• Trough of water• Planes, trains, and automobiles• Rotational related rates

Homework

• 2.6 #3, 7, 13, 15, 18 - 23

Announcements

• Exam – applications of the derivative I –day 5 (this Tuesday)• Quiz – related rates - day 8 (next Sunday)

Period 7 BC Calculus Tuesday 5/11/2008[2.3.5.7.8] day 5

Warm up

• Discuss conclusions of Taylor Polynomial Lab

Exam – applications of the derivative I - 50 minutes

• Finish, correct related rates homework

Homework

• Quiz – related rates - day 8

Announcements

Period 7 BC Calculus Saturday 8/11/2008[2.3.5.7.8] day 7

Warm up – 10 minutes

• Review/correct/discuss exams

Maximum and minimum values – 40 minutes

• What is an absolute max/min?• What is a relative max/min?• What is a critical value?• Extreme Value Theorem and applications

Homework

• 3.1 #15, 23, 28, 33, 36, 39, 42, *45-51odd, *59, *60• * Means calculator okay

Announcements

• Quiz – related rates - day 8• Exam – applications of derivatives II ~ Nov 19

Period 7 BC Calculus Sunday 9/11/2008[2.3.5.7.8] day 8

Warm up – 10 minutes

• Review/correct discuss homework

Rolle’s Theorem and the Mean Value Theorem – 30 minutes

• Remember, these are existence theorems• Definitions• Applications!

Quiz – related rates – 25 minutes

• 3.2 #3, 14, 21, 27, 30, 32, 37, 38, 40, 48, 52, 57, 67• Pay attention to calc/no calc directions• Word problems calculator always okay

Homework

• Exam – applications of derivatives II ~ Nov 19

Announcements

Period 7 BC Calculus Tuesday 11/11/2008[2.3.5.7.8] day 2

Warm up – 10 minutes

• Review/correct quiz

How derivatives affect/reflect the shape of a graph

• Increasing/decreasing• Concavity• Points of inflection• 1st and 2nd derivative tests – clarification of critical values

Homework

• 3.3 #13, 15, 27, 39, 43, 49, 55-63odd, 86• 3.4 #5, 13, 21, 31, 37, 43, 51, 53, 61• Due day 5

Announcements

• Exam – applications of derivatives II ~ Day 8 (Nov 19)• Quiz – curve sketching with and without calculators ~ Nov 24

Period 7 BC Calculus Wednesday 12/11/2008[2.3.5.7.8] day 3

Warm up – 15 minutes

• 3.3 #95, 97, 99• 3.4 #45 - 48

Indeterminate forms and L’Hospital’s Rule

• What is an indeterminate form?• Why does L’Hospital rely on a quotient?• Indeterminate powers

• Note: this ends the applications of derivatives II topics

Homework

• 8.7 #15 – 57 e.o.o.

Announcements

• Exam – applications of derivatives II ~ Nov 19• Quiz – curve sketching with and without calculators ~ Nov 24

Period 7 BC Calculus Sunday 16/11/2008[2.3.5.7.8] day 5

Warm up – 20 minutes

• Preview Amusement park task

Curve Sketching part I – 40 minutes

• How can I use derivative tests to help me graph functions?• How does the second derivative help?• What is the utility of a sign chart?

Homework

• See homework section of handout

Announcements

• Exam – applications of derivatives II ~ Nov 19• Quiz – curve sketching with and without calculators ~ Nov 24

Period 7 BC Calculus Tuesday 18/11/2008[2.3.5.7.8] day 7

Warm up – 15 minutes

• Preview – sample AP questions that may be used as exam questions

Curve Sketching part II – 40 minutes

• How can we increase our understanding of graphs with technology?• How do we graphically communicate information about f from f’ and f’’?

Homework

• See homework section of handout

Announcements

• Exam – applications of derivatives II ~ Nov 19• Quiz – curve sketching with and without calculators ~ Nov 24

Period 7 BC Calculus Wednesday 19/11/2008[2.3.5.7.8] day 8

Warm up – 15 minutes

• Curve sketching homework Q & A

Exam – applications of derivatives II

• Finish curve sketching homework• Review the pre-calculus concepts of polar, vector, and parametric functions

Homework

• Quiz – curve sketching with and without calculators ~ Nov 24

Announcements