# Activities

• • • ##### Subject Area

• Math: Calculus: Applications of the Derivative
• Math: Calculus: Derivatives

• ##### Author 9-12

45 Minutes

• ##### Device
• TI-89 / TI-89 Titanium
• ##### Report an Issue

Higher Order Derivatives #### Activity Overview

Students will calculate the second derivative of functions, inspect a graph and give the intervals for concave up and concave down and find the point of inflection.

#### Key Steps

• Students will explore the higher derivatives of several functions and relate these to the shape of the function graph.

Students will use a nested derivative command to find the second derivative of each function.

• Students will graph the function and its second derivative on the same screen to discover how the function's second derivative relates to the function's shape.

• Students will then find the equation of the tangent line at specific x-values. Students will use this information to find the concavity and point(s) of inflection of the function.