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# Using first derivative. Using second derivative

## 1. 5.3 Differentiation 3

Foundation Year ProgramNUFYP Mathematics

5.3 Differentiation 3

Viktor Ten

2019-2020

## 2. Lecture Outline

Foundation Year ProgramLecture 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 ProgramIntroduction

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 ProgramIncreasing 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