MAT135 Unit 5: Using Derivatives
3.9 LINEAR APPROXIMATION AND THE DERIVATIVE
The Tangent Line Approximation
Estimating the Error in the Approximation
Why Differentiability Makes a Graph Look Straight
The Tangent Line Approximation
Estimating the Error in the Approximation
Why Differentiability Makes a Graph Look Straight
4.1 USING FIRST AND SECOND DERIVATIVES
What Derivatives Tell Us About a Function and Its Graph
Local Maxima and Minima
Finding Local Maxima and Minima
Critical Points: Testing for Local Maxima and Minima
The Second-Derivative Test
Concavity and Inflection Points
How Do We Detect an Inflection Point?
Showing Local Extrema Are at Critical Points
What Derivatives Tell Us About a Function and Its Graph
Local Maxima and Minima
Finding Local Maxima and Minima
Critical Points: Testing for Local Maxima and Minima
The Second-Derivative Test
Concavity and Inflection Points
How Do We Detect an Inflection Point?
Showing Local Extrema Are at Critical Points
4.2 OPTIMIZATION
Global Maxima and Minima
How Do We Find Global Extrema?
Finding Upper and Lower Bounds
Global Maxima and Minima
How Do We Find Global Extrema?
Finding Upper and Lower Bounds
4.3 OPTIMIZATION AND MODELLING
Optimization and Modelling
Graphing Examples
Optimization and Modelling
Graphing Examples
4.4 FAMILIES OF FUNCTIONS AND MODELLING
The Bell-Shaped Curve
Motion Under Gravity
Exponential Model with a Limit
The Logistic Model
The Bell-Shaped Curve
Motion Under Gravity
Exponential Model with a Limit
The Logistic Model
4.6 RATES AND RELATED RATES
Rates and Related Rates
Rates and Related Rates
4.7 L’HOPITAL’S RULE, GROWTH, AND DOMINANCE
L'Hopital's Rule
Dominance
Recognizing the Form of a Limit
L'Hopital's Rule
Dominance
Recognizing the Form of a Limit