# Analysis of Curves

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## Lecture Notes

#### First Derivative Test

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Section 2, Page 1 to page 2

Increasing, decreasing, non-increasing, and non-decreasing functions are defined. First Derivative Test is explained and an example is given.

Instructor: Prof. Jason Starr
Prior Knowledge: Concept of derivative (section 2 of lecture 1)

#### Extremal Points

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Section 3, Page 2 to page 3

Local and global extrema (maxima and minima) are defined. Critical points are defined. Includes short example.

Instructor: Prof. Jason Starr
Prior Knowledge: First Derivative Test (section 2 of this lecture)

#### Concavity and the Second Derivative Test

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Section 4, Page 3 to page 3

Concavity of a function defined as it relates to f, f', and f''. The Second Derivative Test is explained and an example is given.

Instructor: Prof. Jason Starr
Prior Knowledge: Extremal Points and Critical Points (sections 2 and 3 of this lecture)

## Practice Problem

#### Complete Graph Analysis

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Problem 1 (page 1 to page 2)

Graphing a function and finding its asymptotes, maxima, minima, inflection points, and regions where the graph is concave up or concave down.

Instructor: Prof. Jason Starr
Prior Knowledge: None

## Exam Questions

#### Complete Graph Analysis

PDF
Problem 1 (page 1) to problem 2 (page 1)

Two questions which involve sketching the graph of a function, showing all zeros, maxima, minima, and points of inflection.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Complete Graph Analysis

PDF
Problem 1 (page 1)

Sketching a graph and finding the maxima, minima, points of inflection, and regions where the graph is concave up and concave down.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Complete Graph Analysis

PDF
Problem 2 (page 1)

Sketching the graph of a function, including its critical points, points of inflection, and regions where the graph is increasing, decreasing, concave up, or concave down.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Curve Sketching

PDF - 2.2 MB
Problem 2B-1 (page 12) to problem 2B-7 (page 13)

Seven questions which involve sketching graphs and finding inflection points, maxima, and minima as well as regions where a function is increasing, decreasing, or zero.

Instructor: Prof. David Jerison
Prior Knowledge: None