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Brief Review
Chapter 3 – Applications of the Derivative
3.1: Extrema of a Function
3.2: First Derivative Test
3.3: Concavity and the Second Derivative
- 01) Higher Order Derivatives
- 02) Example 2
- 03) Example 3
- 04) Example 4
- 05) Concavity and Points of Inflection
- 06) Concavity and 2nd Derivative
- 07) Example 5
- 08) 2nd Derivative Test for Relative Extrema
- 09) Example 6
- 10) Example 8
- 11) Example 10
- 12) Example 11
- 13) Example 12
- 14) Implicit Differentiation
- 15) Calculator Example
3.4: Geometric Optimization Problems
3.5: Business and Economic Optimization Problems
3.6: Linearization and Differentials
- 01) Linearization
- 02) Example 1
- 03) Examples 2 and 3
- 04) Differentials
- 05) Example not in textbook
- 06) Example 5: Bacteria
- 07) Relative Change
- 08) Analysis of E
- 09) Differential Formulas
Chapter 4 – Exponential and Logarithmic Functions
4.1: Inverse Functions
4.2: Exponential Functions
4.3: The Number e
4.4: The Derivative of e
4.5: Logarithmic Functions
- 01) Introduction to Logs
- 02) Decay Example: Solve for t, Part 1
- 03) Decay Example: Solve for t, Part 2
- 04) Inverse y equals 2 to x
- 05) Inverse y equals 10 to x
- 06) Practice evaluating logs
- 07) Calc. Practice: Napiers Bones
- 08) Logorithms ph
- 09) Graphs and transformation
- 11) y equlas in plus minus e
- 12) Derivative of f of x
- 13) Generalized Logorithmic
- 14) Calculator Example
- 15) Calculator Example 2
- 16) Calculator Example 3
4.6: Properties of Logarithmic Functions
- 01) Properties of Logs
- 02) Multiplication Property of Logs
- 03) Division Property of Logs
- 04) Practice with Properties
- 05) Discovering Exponential Property
- 06) Using the Property
- 07) Derivatives Using Properties
- 08) Solving Logarithmic Equations
- 09) Solving Exponential Equations
- 10) t in Compound Interest Problems
- 11) Solving for r and t
- 12) Change of Base
- 13) Derivative and Change of Base
- 14) Logarithmic Differentiation
- 15) Calculator Example
4.7: Applications of Exponential and Logarithmic Functions
- 01) Introduction
- 02) Investment Example
- 03) Bacterial Growth Example
- 04) Radioactive Decay
- 05) Carbon Dating
- 06) Logistical Growth and Richtor Scale
- 07) Sea Lion Hint
- 08) Calculator Example
Chapter 5 – Integration and its Applications
5.1: Antidifferentiation – Integration
5.2: Applications of Antidifferentiation
5.3: The Substitution Method
5.4: Approximation of Areas
5.5: Sigma Notation and Areas
5.6: The Definite Integral
5.7: Substitution and Properties of the Definite Integral
5.8: Applications of the Definite Integral
- 01) Introduction
- 02) Example 1
- 03) Example 2
- 04) Example 3
- 05) Consumer Surplus
- 06) Producer Surplus
- 07) Continuous Income Flow
- 08) Probability Density Functions
- 09) Calculator Example
- 10) Calculator Example 2
- 11) Calculator Example 3
- 12) Calculator Example 4
Chapter 6 – An Introduction to Functions of Several Variables
6.1: Functions of Several Variables
6.2: Partial Derivatives
- 01) Notation and Example 1
- 02) Examples 2 and 3
- 03) Visualization and Example 4
- 04) Examples 5 and 6
- 05) Level Curves / Contours
- 06) Example 7
- 07) Cobb Douglas Production Function
- 08) Example 8
- 09) Example 9
- 10) Level Indifference Curve
- 11) Utility Function Example
- 12) Higher Order Example 1
- 13) Higher Order Example 2
- 14) Calculator Example
6.3: Extrema
6.4: The Method of Lagrange Multipliers
6.5: Economic Applications
- 01) Product Example 1
- 02) Product Example 2
- 03) Product Example 3
- 04) Cobb Douglas Production Example
- 05) The Marginal Rate of Substitution
- 06) Utility Function Example