5.3 Differentiation 3
Lecture Outline
Introduction
Increasing and decreasing functions
Increasing and decreasing functions
Increasing and decreasing functions
Increasing and decreasing functions
Increasing and decreasing functions
Increasing and decreasing functions
Increasing and decreasing functions
Increasing and decreasing functions
Increasing and decreasing functions
Increasing and decreasing functions
Increasing and decreasing functions
Concavity
Concavity
Concavity
Inflection points
Inflection points
Inflection points
Inflection points
Relative (Local) Maxima and Minima
Relative (Local) Maxima and Minima
Relative (Local) Maxima and Minima
Relative (Local) Maxima and Minima
Relative (Local) Maxima and Minima
Relative (Local) Maxima and Minima
Relative (Local) Maxima and Minima
Relative (Local) Maxima and Minima
Relative (Local) Maxima and Minima
Relative (Local) Maxima and Minima
First derivative test
First derivative test
First derivative test
First derivative test
First derivative test
Second derivative test
Second derivative test
Second derivative test
Second derivative test
Second derivative test
Learning outcomes
Formulae
Formulae
Preview activity: Differentiation 4
2.22M
Category: mathematicsmathematics

Using first derivative. Using second derivative

1. 5.3 Differentiation 3

Foundation Year Program
NUFYP Mathematics
5.3 Differentiation 3
Viktor Ten
2019-2020

2. Lecture Outline

Foundation Year Program
Lecture Outline
Using
first derivative
Using
second derivative
Increasing/
decreasing intervals
Concavities
Critical points
• Stationary points
First derivative test
Inflection points
Second derivative test
2019-2020

3. Introduction

Foundation Year Program
Introduction
The purpose of this lecture is to develop mathematical tools
that can be used to determine the exact shape of a graph
and the precise locations of its key features such as local
extremes, inflections, intervals of increasing/decreasing,
upward/downward concavities.
2019-2020

4. Increasing and decreasing functions

Foundation Year Program
Increasing and decreasing functions
The terms increasing, decreasing, and constant are used to describe
the behavior of a function as we travel left to right along its graph.
The function in the figure can be described as
increasing to the left of
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