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Lecture Notes
PDF
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.
Prof. Jason Starr
Concept of derivative (section 2 of lecture 1)
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PDF
Section 3, Page 2 to page 3
Local and global extrema (maxima and minima) are defined. Critical points are defined. Includes short example.
Prof. Jason Starr
First Derivative Test (section 2 of this lecture)
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PDF
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.
Prof. Jason Starr
Extremal Points and Critical Points (sections 2 and 3 of this lecture)
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Practice Problem
PDF
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.
Prof. Jason Starr
None
Solution (PDF) Pages 8 to 9
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Exam Questions
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.
Prof. David Jerison
None
Solution (PDF)# Page 1
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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.
Prof. David Jerison
None
Solution (PDF)# Page 1
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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.
Prof. David Jerison
None
Solution (PDF)# Page 1
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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.
Prof. David Jerison
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PDF
Problem 2 (page 3 to page 5)
Eight-part problem which involves sketching a graph and finding the asymptotes, maxima, minima, and inflection points of the graph.
Prof. Jason Starr
None
Solution (PDF) Pages 2 to 4
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