Unit route
Study lessons in order, complete the pathway selected by diagnostic evidence, conduct the investigation, then demonstrate mastery. Reassessment follows correction and reflection.
Weeks 10, 11, 12 · 7 detailed lessons
The Derivative from First Principles
How does the limiting slope of secant lines define instantaneous change?
Pathways
Lesson 01 · Week 10
Secant Slopes and Average Change
The derivative is the limit of average rates of change over shrinking intervals. Geometrically it is tangent slope; contextually it is instantaneous rate with output units divided by input u…
Lesson 02 · Week 10The Difference Quotient
The derivative is the limit of average rates of change over shrinking intervals. Geometrically it is tangent slope; contextually it is instantaneous rate with output units divided by input u…
Lesson 03 · Week 10Derivative as a Limit
The derivative is the limit of average rates of change over shrinking intervals. Geometrically it is tangent slope; contextually it is instantaneous rate with output units divided by input u…
Lesson 04 · Week 11Tangent Lines and Local Linear Behavior
The derivative is the limit of average rates of change over shrinking intervals. Geometrically it is tangent slope; contextually it is instantaneous rate with output units divided by input u…
Lesson 05 · Week 11Differentiability and Corners, Cusps & Vertical Tangents
The derivative is the limit of average rates of change over shrinking intervals. Geometrically it is tangent slope; contextually it is instantaneous rate with output units divided by input u…
Lesson 06 · Week 12Derivative Notation, Units & Interpretation
The derivative is the limit of average rates of change over shrinking intervals. Geometrically it is tangent slope; contextually it is instantaneous rate with output units divided by input u…
Lesson 07 · Week 12Estimating and Sketching Derivatives from Graphs
A derivative graph records the slope of the original function. Positive derivative values correspond to increasing behavior, zeros often correspond to horizontal tangents, and derivative mag…