5.3 Maximizing Profitap Calculus


Chapter 9: Profit Maximization Profit Maximization The basic assumption here is that firms are profit maximizing. Profit is defined as: Profit = Revenue – Costs Π(q) = R(q) – C(q) Π(q) =p(q)⋅q −C(q) To maximize profits, take the derivative of the profit function with respect to q and set this equal to zero. Maximize Slope Directions: Given the point (3,5), use digits 1-9, at most one time, to find a point (, ) that maximizes the slope of the line that passes through the two points. The slope cannot be undefined. Profit Maximization given Profit and Cost Functions Please accept statistics, marketing cookies to watch this video. Profit maximization is one of the topics that are likely to be tested in the short-answer section of the AP Calculus exam. It is equal to a business’s revenue minus the costs incurred in producing that revenue.


The topics below are both AB and BC topics. The topics preceded with an asterisk (*) are BC only topics. All documents are .pdf

Course Info:

1st Day Handout: Parent/Student Letter

1st Day Homework: Academic Integrity, Parent Survey, Student Survey

AP Calculus Syllabus: AB, BC

Open House Info: AB & BC, Bingo, & Schedule

AP Calculus Survival Guide

Getting Ready:

Appendix: Precalculus stuff to know cold (Notes)

Appendix: Parent Function Catalog (Notes)

Appendix: The Unit Circle (Notes)

Spleen: Prerequisite Algebra Skills (WS/KEY)

Chapter P: Calculus Prerequisites

P.1 What is AP Calculus? (Notes)

P.2 Parent Functions (Notes, WS/KEY)

P.3 Simplifying Expressions (Notes, WS/KEY)

P.4 Equations of Lines (Notes, WS)

P.5 Domain, Range, and Symmetry (Notes, WS)

P.6 Fun with Functions (Notes, WS)

P.7 Trigonometry (Notes, WS)

Chapter 1: Limits

1.1 Limits & Continuity (Notes/E01/E02-06/E07-09/E010-11/E11-12a/E12b-13, WS/KEY)

1.2 Properties of Limits (Notes/E01-02/E03/, WS/KEY)

1.3 Limits at Infinity (Notes/E01-02/E03-04/E04intro/E04-05/E06-07/, WS/KEY)


1.4 Algebraic Limits (Notes/E01-06/E07/E08-12a/E12b-13a/E13b-15d/E15e-h/E15i-16e/E16/, WS/KEY)

1.4 Xtra Practice (WS/KEY)

1.5 Continuity on Intervals & IVT (Notes/E01-03/E03-06b/E6-10/, WS/KEY)

Chapter 2: Differentiation

2.1 Tangent Line & Differentiability (Notes/E01/E01-03/E04-06/E07-09/E10/E11-13/E12-14, WS/KEY)

2.2 Derivatives on the Calculator (Notes/EA/, WS/KEY)

2.3 Basic Differentiation Rules (Notes/E01-06/E07-10/E10-12/E11-12/E13/, WS/KEY)

2.4 Product & Quotient Rules (Notes/E01/E02-03/E04/E05-08/E08-10/E11/, WS/KEY)

2.5 Rates of Change and Particle Motion I (Notes/E01-05/E06/E07-08/E09/, WS/KEY)


2.6 The Chain Rule (Notes/E01a/E01b-f/E01g-04/E05-08/, WS/KEY)


2.7 Implicit Differentiation (Notes/E01-03/E03-06/07a-c/07d-09/E10/, WS/KEY)

2.8 Derivatives of Inverse & Inverse Trig Functions (Notes/E01/E02-03/E4-9/E08-10/E11-13/, WS/KEY)

2.9 Derivatives of Exponential Functions (Notes/E01/E02-05c/E05d-e/E06-07/E08-10/, WS/KEY)

2.10 Derivatives of Log Functions & LOG DIFF (Notes/E01-06/E07-12/, WS/KEY)

Chapter 3: Applications of Differentiation

3.1 Extrema on an interval (Notes/E1-3/E4-6/E7-8/E9/E10-11/, WS/KEY)

3.2 Rolle's Theorem and the MVT (Notes/E1-2/E3-5/E6/E7/, WS/KEY)

3.3 Increasing, Decreasing, and 1st Derivative Test (Notes/E1-2/E3/E4-5/E6-7/E8/, WS/KEY)

3.4 Concavity and the Second Derivative Test (Notes/E1-2/E3-4a/E4b-c/E4d-e/E4f-6c/E6d-7d/E7e-8/, WS/KEY)

3.5 f, f ', and f '(Notes/E1-2b/E1/E2/E3-4/, WS/KEY)

3.5B Summary Sheet (Notes)

3.6 Optimization (Notes/E1/E1-2/E2-6/E6-9/E10-11/E13-14/, WS/KEY)

3.7 Linearization and Differentials (Notes/E1-2/E3-6, WS/KEY)

3.8 Related Rates (Notes/E1-3/E4-5/E6-7/E8-11/, WS/KEY)

Chatper 4: Integration

4.1 Antiderivatives and Indefinite Integration (Notes/E1-3/E4/E5-6d/E6e-f/, WS/KEY)

4.1B Basic Differentiation Practice (WS/KEY)

4.1C Mixed AP MC Review (WS)

4.2 Numeric Definite Integrals (Notes/E1/E2a-c/E2d-3/E4-7/E8-9/E10-13/E14/, WS/KEY)

5.3 Maximizing Profitap Calculus Solver

4.3 The FTOC I & II and MVT II (Notes/E1/E1b-4/E5-9a/E8-11/E12-13/E14-17/E18-20/E21/, WS/KEY)

4.4 Integration by u-Substitution (Notes/E1-4/E3-8/E9-13/E13-18b/E18b-24a/E24bce/E24d-25/E24c-e/E25-26, WS/KEY)

Chapter 5: Differential Equations & Modeling

5.1 Separable Differential Equations (Notes/E1-3/E4-8/E9-12/, WS/KEY)

5.2 Slope Fields (Notes/E1-7/E8-17/, WS/KEY)

5.2B Mega Integration Practice (AB methods) (WS)

5.3 *Euler's Method (Notes/E1a/E1b-4/, WS/KEY)

5.4 *Integration by Parts (Notes/E1-8/E8-12/E12-13/, WS/KEY)

5.5 *Partial Fractions & Logistic Growth (Notes/E1-3/E4-8b/, WS/KEY)

Chapter 6: Applications of Integration

6.1 Integral as Net Change (Notes/E1-3/E4-5/E6-7/E9, WS/KEY)

6.2 Area between Curves (Notes/E1-5/E4-7a/E5-7/E8/, WS/KEY)

6.3 Volumes (Notes/E1-4/E4-7c/E7-8/E7d-8a/E8b-9/E10-10c/, WS/KEY)

6.4 *Arc Length (Notes/E1-2/E3-6, WS/KEY)

6.5 L'Hôpital's Rule and Indeterminate Forms (Notes/E1-3b/E3c-d/4-5/6-7b/7c-9/, WS/KEY)

6.6 *Improper Integrals (Notes/E1-3/E4-7/E8-11b/E11c-15/E16-19, WS/KEY)

Chatper 7: Vector Calculus

7.1 *Intro to Parametric & Vector Calculus (Notes/E1-3/E4-9, WS/KEY)

5.3 Maximizing Profitap Calculus Calculator

7.2 *Parametric & Vector Accumulation (Notes/E1-2, WS/KEY) Worksheet II/KEY

Chapter 8: Polar Calculus

5.3 maximizing profitap calculus solver

8.1 *Polar Intro & Derivatives (Notes/E1-2a/E2b-3/E4-7a/E7b-10/, WS/KEY)


8.2 *Polar Area (Notes/E1-2/E3-6/E7-8, WS/KEY)

Chapter 9: Sequences & Series

9.1 *Infinite Sequences & Series (Notes/E1-4/E5-8/E9-11/E12-15/E16-20a/E20b-22, WS/KEY)

Summary of Tests for Convergence and Series Flow Chart with practice problems

9.2 *Taylor Polynomials (Notes/E1-3/E4-8/, WS/KEY)

9.3 *Power Series I: Taylor & Maclaurin Series (Notes/E1-2a/E2a-2d/E3-5/E6-9/, WS/KEY)

9.4 *Power Series II: Geometric Series (Notes/E1-7/E7-11/E12/E13/, WS/KEY)

9.5 *Lagrange Error Bound (Notes/E1-4/E5, WS/KEY)

Chapter 10: After the AP Exam

10.1 Trig Substitution Integration (Notes/KEY, WS/KEY)

10.2 Partial Fraction Decomposition (Notes/KEY, WS/KEY)

10.3 Epsilon-Delta Proofs (Notes/KEY, WS/KEY)

5.3 Maximizing Profitap Calculus 14th Edition

10.4 Newton's Method (Notes/KEY, WS/KEY)

10.5 Surface Area (Notes/KEY, WS/KEY)

10.6 Hyperbolic Trig Functions (Notes/KEY, WS/KEY)