Study Guide

# Derivatives Topics

### Derivative as a Limit of Slopes

The derivative of the function f at x = a is the slope of...

### Derivatives as an Instantaneous Rate of Change

Here we'll approach the derivative from a different and more real-lifey direction.There are two...

### Tangent Lines

Daisy, our favorite track star, is learning how to throw discus via Youtube videos. She...

### Tangent Line Approximation

There are only two things we need to remember about the tangent line to f at a. The tangent line...

### Differentiability and Continuity

We've had all sorts of practice with continuous functions and derivatives. Now it's time to see...

### The Derivative Function

The "derivative of f at a," written f ' (a), is a number that is equal to the slope of the...

### Graphs of f ( x ) and f ' ( x )

From a graph of a function f(x) we can sketch graph of its derivative f ' (x). To do this,...

### Theorems

Rolle's Theorem says:Let f be a function that is continuous on the closed interval...

### In the Real World

Derivatives are, believe it or not, used a lot. The field of differential equations is an area of...