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Mathematics lessons for IB® Diploma Programme

Analysis and Approaches | Calculus

Graphing_Relationships_5

Graphing Relationships

Activity Overview

In this activity, students explore information about a graph based on the first and second derivatives. They learn that a function's derivative is positive when the function increases and negative when the function decreases. They learn that the second derivative is positive when the graph is concave upward and negative when the graph is concave downward.

Key Steps

Graphing_Relationships_3

Step 1

Students will learn that a function’s derivative is positive when the function increases and negative when the function decreases.

Graphing_Relationships_5

Step 2

Students will learn that the second derivative is positive when the graph is concave upward and negative when the graph is concave downward.