Part 1/6:

Understanding the Second Derivative Test: A Concise Guide

In this article, we delve into the second derivative test, exploring its significance in determining the behavior of graphs, including concepts of concavity, inflection points, and local maxima and minima.

Introduction to Concavity

Concavity refers to the way a curve bends; a function can be either concave upwards or concave downwards.

Concave Upwards: A function is concave upwards if the slope of the tangent line is increasing. Visually, this appears as a "U" shape.
Concave Downwards: Conversely, a function is concave downwards if the slope of the tangent line is decreasing, resembling an "n" shape.

Understanding the concavity of a function can be systematically analyzed using its first and second derivatives.