Optimization and Derivatives
The Calculus of Finding Minima
Build from scratch the calculus tools needed for optimization: limits, continuity, derivatives, and differentiability. Understand local linear approximation and the hierarchy of function classes C⁰, D¹, and C¹.
Sections
Optimization Problems
8 min · 2 quiz questions
Why We Need Derivatives
7 min · 2 quiz questions · Interactive diagram
Functions of One Variable
6 min · 2 quiz questions
Multivariate Functions
6 min · 2 quiz questions
The Limit Concept
8 min · 2 quiz questions
Left- and Right-Hand Limits
7 min · 2 quiz questions
Limits at Infinity
6 min · 2 quiz questions
Formal Definition of Limit
8 min · 2 quiz questions
Continuity
8 min · 2 quiz questions · Interactive diagram
Rate of Change
8 min · 2 quiz questions · Interactive diagram
The Derivative
10 min · 2 quiz questions · Interactive diagram
When the Derivative Does Not Exist
8 min · 2 quiz questions
Derivative Notations
5 min · 2 quiz questions
Differentiation Rules
10 min · 2 quiz questions · Interactive diagram
The Derivative as a Function
7 min · 2 quiz questions
Symbolic Differentiation
7 min · 2 quiz questions
Continuously Differentiable Functions (C¹)
7 min · 2 quiz questions
Local Linear Approximation
10 min · 2 quiz questions · Interactive diagram
Approximation Error
8 min · 2 quiz questions · Interactive diagram
Differentiability vs Continuity
7 min · 2 quiz questions
Class Inclusions C⁰ ⊃ D¹ ⊃ C¹
8 min · 2 quiz questions