# Unit 3

## Intro

Derivatives have many mathematical applications. They can be used to find limits of indeterminate expressions, find extrema, intervals of increasing/decreasing, inflection points, and concavity.

Extrema are a fancy word for extreme values. This can either be minimum values (minima) or maximum values (maxima).

Intervals of increasing/decreasing are the parts of a graph of a function in which it is going up or going down.

Inflection points are points in which the concavity (bending) of a graph of function is changing. Concavity of a graph of a function can either be bending up (concave up) or bending down (concave down).

Ultimately, the most important feature of differentiation is the optimization of a system. This deals with finding the most optimal constraints on a system.

## Unit 3 Podcast (coming soon)

## Using Derivatives to Find Limits

## Behavior of Graphs

## Real World Applications

## Theorems

## Videos

### 3.A. L'Hospital's Rule

### 3.B. Increasing/Decreasing Intervals and Extrema & Critical Numbers

**Extreme Values (Extrema) (conceptual)****Absolute and Relative Extrema (conceptual)****Critical Numbers (conceptual)****Extrema (example problem 1 of 4)****Extrema (example problem 2 of 4)****Extrema (example problem 3 of 4)****Extrema (example problem 4 of 4)****Increasing and Decreasing Functions (conceptual)****Increasing and Decreasing Functions and Extrema (example problem 1)****Increasing and Decreasing Functions and Extrema (example problem 2)****Increasing and Decreasing Functions and Extrema (example problem 3)**

### 3.C. Concavity and Inflection Points

### 3.D. Physics of Basic Motion

**coming soon...**

### 3.E. Related Rates

### 3.F. Optimization

**coming soon...**