Education Technology

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

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    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.

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    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.

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    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.