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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