Course: Calculus I
Topic: Analysis of Curves
Subtopic: Second Derivative Test & Concavity


The second derivative gives information about the nature of a function including inflection points and concave up/down regions of a curve. Concavity is describes the shape of a region of a curve, basically measuring if it is like a right side up cup or an upside down cup. Inflection points (IPs) are points where the concavity of a curve changes. The second derivative test enables us to determine if a critical point is a relative minimum or relative maximum using information about concavity of the curve where the CP lies.


By the end of this topic you should know and be prepared to be tested on:


Terms you should be able to define: concavity, inflection point (IP), second derivative test

Mini-Lectures and Examples

STUDY: Analysis of Curves - 1st and 2nd Deriv Tests, IPs, Concavity

Supplementary Resources (optional)

Video: Concavity and the Second Derivative Test, Selwyn Hollis's Video Calculus

Lesson: The Second Derivative and the Shape of f, Dale Hoffman's Contemporary Calculus

rev. 2020-10-31