Course: Calculus I
Topic: Analysis of Curves
Subtopic: First Derivative Test & Increasing/Decreasing Functions


The first derivative gives information about the nature of a function including critical points and increasing/decreasing regions of a curve. Critical points (CPs) are points where the first derivative is zero or undefined thereby providing information about the tangent line at a CP which could be horizontal, vertical, or impossible. A region of a curve that is going up up up as you look at it from left to right is increasing and, similarly, one that goes down down down is decreasing. The first derivative test enables us to determine if a critical point is a relative minimum or relative maximum using information about the increasing/decreasing nature 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: increasing, decreasing, strictly monotonic, critical point (CP), horizontal tangent line (HTL), vertical tangent line (VTL), cusp, sharp corner, first derivative test

Mini-Lectures and Examples

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

Supplementary Resources (optional)

Video: Critical Numbers and the First Derivative Test, Selwyn Hollis's Video Calculus

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

rev. 2020-10-31