Analysis of Curves

First Derivative Test

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

• 18.01 Single Variable Calculus, Fall 2005
  Prof. Jason Starr

Course Material Related to This Topic:

• Read lecture notes, section 2 on pages 1–2

Extremal Points

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

• 18.01 Single Variable Calculus, Fall 2005
  Prof. Jason Starr

Course Material Related to This Topic:

• Read lecture notes, section 3 on pages 2–3

Concavity and the Second Derivative Test

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

• 18.01 Single Variable Calculus, Fall 2005
  Prof. Jason Starr

Course Material Related to This Topic:

• Read lecture notes, section 4 on page 3

Complete Graph Analysis

• 18.01 Single Variable Calculus, Fall 2005
  Prof. Jason Starr

Course Material Related to This Topic:

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

• Complete practice problem 1 on pages 1–2
• Check solution to practice problem 1 on pages 8–9

Eight-part problem which involves sketching a graph and finding the asymptotes, maxima, minima, and inflection points of the graph.

• Complete exam problem 2 on pages 3–5
• Check solution to exam problem 2 on pages 2–4

• 18.01 Single Variable Calculus, Fall 2006
  Prof. David Jerison

Course Material Related to This Topic:

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

• Complete exam problems 1 to 2 on page 1
• Check solution to exam problems 1 to 2 on page 1

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

• Complete exam problem 1 on page 1
• Check solution to exam problem 1 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.

• Complete exam problem 2 on page 1
• Check solution to exam problem 2 page 1

Curve Sketching

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.

• 18.01 Single Variable Calculus, Fall 2006
  Prof. David Jerison

Course Material Related to This Topic:

• Complete exam problems 2B–1 on page 12 to problems 2B–7 on page 13
• Check solution to exam problems on pages 19–23