# Higher-Order Derivatives

Taught by Houston
• Currently 4.0/5 Stars.
3122 views | 2 ratings
Meets NCTM Standards:
Lesson Summary:

In this lesson, we explore higher-order derivatives and their practical applications. We define the second, third, and fourth derivatives, and show how they can be used to determine graph concavity and local approximations by linear, quadratic, and cubic polynomials. We also provide examples of how to calculate the linear and quadratic approximations and how they can be used to approximate values of functions. Ultimately, this lesson provides a deeper understanding of graph behavior and how to accurately approximate them with polynomials.

Lesson Description:

Higher-order derivatives. Concavity. Local approximation by linear, quadratic, and cubic polynomials.

Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.

• How do you find higher-order derivatives?
• How do you find the third derivative of a function?
• How do you find the fourth derivative of a function?
• What does it mean for a graph to be concave up or concave down?
• What is an inflection point?
• What is linear approximation?
• 