Critical Numbers and the First Derivative Test
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Lesson Description:
Critical numbers of a function. The first derivative test for local extrema.
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.
Additional Resources:
- Increasing and Decreasing Functions - Practice with Increasing and Decreasing Functions.
- Local Extreme Values (critical numbers) - Practice with Local Extreme Values (critical numbers).
Questions answered by this video:
- What is a critical number?
- What is the first derivative test?
- What is a local extreme value?
- How do you find local minimum and local maximum values of a function?
- How do you pick test points for critical points?
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Staff Review
Discussed in this video are critical numbers, critical points, and how to determine whether a point of a function is a local minimum, local maximum, or neither using the first derivative test. Several examples are done, and the common, accepted method for making a sketch of fâ(x) for critical points is shown, as well as picking test points and determining local minimum and local maximum points for the function. This is a truly useful video for any Calculus student. -
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