**Application of Derivatives**

Maximums, Minimums, and Particle Motion

Learn how to find extrema using the First and Second Derivative Tests. Use derivatives to solve Optimization problems. Investigate velocity, acceleration and speed as well as the graph of the derivative.

## Application of Derivatives Lesson 1

1 hr 53 min 4 Examples

- Curve Sketching Overview
- First Derivative Test and Second Derivative Test
- Justifying critical values, increasing and decreasing intervals, and maximums and minimums
- Justifying inflection points and concavity
- Examples of Curve Sketching (4 examples)

## Application of Derivatives Lesson 2

1 hr 48 min 15 Examples

- Intermediate Value Theorem
- Mean Value Theorem (1 example)
- Rolle’s Theorem (3 examples)
- Absolute Extrema (2 examples)
- Optimization (7 examples)

## Application of Derivatives Lesson 3

1 hr 29 min 21 Examples

- Overview of Graphing Derivatives
- Sketching the graph of a derivative (7 examples)
- Using techniques of graphing derivatives in multiple choice questions (6 examples)
- Particle Motion and Extrema Overview
- Finding Velocity and Acceleration
- Finding when a particle/object is at rest
- Finding when a particle/object changes direction
- Finding speed
- Example of how we combine graphing derivatives with particle motion

## Demand Function

1 hr 20 min 9 Examples

- Example #1: Find marginal profit
- Example #2: Find Cost, Average Cost, Marginal Cost and Minimum Average Cost
- Example #3: Maximize Profit
- Example #4: Determine product level that will Maximize Profit
- Example #5: Find the Demand Function
- Example #6: Find Demand Function, Revenue Function and maximum rebate
- Example #7: Maximize Revenue
- Example #8: Find Cost, Average Cost, Marginal Cost and Minimum Average Cost
- Example #9: Determine product level that will Maximize Profit

## Elasticity of Demand

30 min 5 Examples

- Examples #1-2: Find the Elasticity and interpret your results
- Example #3: Find Elasticity given demand function and interpret results
- Example #4: Find Elasticity. Will an increase in price increase revenue?
- Example #5: Find Elasticity. Should a hotel raise it’s prices?