Using the First Derivative Test to Determine Relative (Local) Extrema
Samuel Baker
6 min read
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Study Guide Overview
This study guide covers the First Derivative Test for finding relative extrema (maxima and minima) of functions. It explains how to find critical points by setting the derivative equal to zero and analyzing the sign of the derivative around these points to classify them. The guide includes a walkthrough example with f(x) = x² and practice problems to apply the concept.
#5.4 Using the First Derivative Test to Determine Relative (Local) Extrema
Welcome back to Calculus with Fiveable! Let’s get into it.
Can the derivative of a function give us more information than just where the function increases or decreases? Yes, it can! In this study guide, we’ll learn how you can use the derivative of a function to determine its relative or local extrema.
#🥇 First Derivative Test
We can use the First Derivative Test to determine the relative (local) extrema of a function. It states that if the derivative of a function changes from positive to negative at a point (which means that the function changes from increasing to decreasing at the point), then the function has a local or relative maximum at that point. If the derivative changes from negative to positive at a point (which means that the function changes from decreasing to increasing at the point), then the function has a local or relative minimum at that point.
The process...
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