Applications of Derivatives

Curve Sketching with Derivatives

Extreme Value Theorem

Applying the Extreme Value Theorem

Finding Critical Numbers

Maxima, Minima, and Critical Points

Finding Relative Max/Min Values

Finding Maxima and Minima Example

Mean Value Theorem

Intuition Behind the Mean Value Theorem

Finding Where the Derivative is Equal to the Average Rate of Change

Concavity

Recognizing Concavity

Points of Inflection

Graphing with Derivatives- Example 1

Graphing with Derivatives- Example 2

Linearization/Optimization/Related Rates

Tangent Line Approximation

Linearization

Local Linearization

Linearization Example

Newton’s Method

Optimization

Optimization- Example Volume of Box

Optimization- Example Maximize Profit

Optimization- Example Minimize Cost

Related Rates

Related Rates- Example Change in Balloon Height

Related Rates- Example Water from an Inverted Cone

Related Rates- Example Distance Between Cars

Related Rates- Example Shadow from Lamp Post

Class Notes (Coming Soon)