## Derivatives, their Graphs, & Particle Motion

In Chapter 2, we learned how to find the slope of a tangent to a curve as the limit of the slopes of the secant lines. The study of rates of change of functions is called

*differential calculus*, where the*derivative*simply represents the slope of the tangent line of a function at any given point. The derivative was the 17th-century breakthrough that enabled mathematicians to unlock the secrets of planetary motion and gravitational attraction -- of objects changing position over time. In this chapter we will concentrate on understanding what derivatives are and how they look.## Key Words and Vocabulary

Definition of Derivative

Notation

Relationships between f(x) and f'(x)

Graphing the Derivative from Data

One-Sided Derivatives

How f'(a) Might Fail to Exist

Differentiability Implies Local Linearity

Derivatives on a Calculator

Differentiability Implies Continuity

IVT for Derivatives

Positive Integer Powers, Multiples, Suns and Differences

Products and Quotients

Negative Integer Powers of x

Second and Higher Order Derivatives

Instantaneous Rates of Change

Motion along a Line

Sensitivity to Change

Derivatives in Economics

Analyzing Velocity, Acceleration & Speed

Notation

Relationships between f(x) and f'(x)

Graphing the Derivative from Data

One-Sided Derivatives

How f'(a) Might Fail to Exist

Differentiability Implies Local Linearity

Derivatives on a Calculator

Differentiability Implies Continuity

IVT for Derivatives

Positive Integer Powers, Multiples, Suns and Differences

Products and Quotients

Negative Integer Powers of x

Second and Higher Order Derivatives

Instantaneous Rates of Change

Motion along a Line

Sensitivity to Change

Derivatives in Economics

Analyzing Velocity, Acceleration & Speed

## Downloadable Documents

**Chapter 3 Part 1 Supplemental Note Inserts:**

ch_3_pt_1_note_supplement_2014.pdf | |

File Size: | 2324 kb |

File Type: |

**Chapter 3 Part 2 Supplemental Note Inserts:**

ch_3_pt_2_note_supplement_for_jodi.doc | |

File Size: | 840 kb |

File Type: | doc |

## Screencasts

## Resources

This video describes how to sketch f(x) given a graph or description of the derivative.

This video is helpful if you get stuck on 3.1B #13-16. The video describes how to match a f(x) graph with its f'(x) graph.

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