| Applications of Differentiation |
| Day |
Notes |
Critical Homework |
Videos |
| 1 |
Extrema on an Interval |
Lesson 1 |
Solutions |
Extreme Value Theorem |
| Applying the Extreme Value Theorem |
| Finding Critical Numbers |
| 2 |
Rolle’s Theorem & Mean Value Theorem(MVT) |
Lesson 2 |
Solutions |
Rolle's Theorem (and proving a horiz. tangent line) |
| Theory behind the Mean Value Theorem |
| Applying the Mean Value Theorem Example |
| 3 |
Increasing and Decreasing Functions & The First Derivative Test |
Lesson 3 |
Solutions |
Intervals of Increase/Decrease |
| Finding Intervals of Increase/Decrease and Local Min/Max. |
| AP Example of Finding Intervals of Increase |
| Using First Derivative Test to Determine Relative Min/Max. |
| Interpreting the First Derivative Graph |
| Examples of Reading a First Derivative Graph to Determine Qualities of the Original Graph |
| 4 |
Concavity & the Second Derivative Test |
Lesson 4 |
Solutions |
Concavity and Inflection Points |
| Finding Intervals of Concavity(Up & Down) |
| Finding Intervals of Concavity Using the First Derivative Graph |
| Analyzing Concavity (Graphical) |
| 5 |
Linearization and Tangent Line Approximation |
Lesson 5 |
Solutions |
Tangent Line Approximation |
| Tangent Line Approximation Examples |
| 6 |
Optimization |
Lesson 6 |
Solutions |
Optimization Procedures/Plan |
| Optimization |
| Optimization of Profit |
| Optimization of Geometry |
| Optimization of Volume (1 With Calculator) & (2 with Calculus) |