Higher-Order Derivatives
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.
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.
- The d/dx Notation; Higher Order Derivatives - Practice with d/dx Notation and Higher Order Derivatives.
- 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?
- What is quadratic approximation?
- How do you find the linear and quadratic approximations of functions at a value?
- What is cubic approximation?
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Staff Review
In this video, you will learn how to find the second, third, fourth, and higher derivatives of functions, including polynomials trig functions, and square root functions. Also, you will learn what the derivatives mean graphically. Some of the graphs shown are really interesting and helpful for understanding what is really going on with first and second derivatives, concavity, and inflection points. Linear, quadratic, and cubic approximations of functions are also found and shown graphically. A really interesting video.
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