Critical Numbers and the First Derivative Test
In this lesson, we learn about critical numbers and the first derivative test. A critical number is a point where the derivative of a function equals zero or is undefined. The first derivative test allows us to classify critical points as local maxima, local minima, or neither. By analyzing the sign of the derivative near each critical point, we can determine the nature of the critical point. This lesson includes several examples that demonstrate how to find and classify critical numbers.
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.
- Increasing and Decreasing Functions - Practice with Increasing and Decreasing Functions.
- Local Extreme Values (critical numbers) - Practice with Local Extreme Values (critical numbers).
- 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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