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First Derivative Test

Definition

The First Derivative Test is a method used to determine the intervals on which a function is increasing or decreasing, and to identify local extrema (maximum or minimum) points.

Analogy

Imagine you are driving a car on a hilly road. The First Derivative Test tells you when you are going uphill (increasing) or downhill (decreasing), and it also helps you spot the highest point (maximum) or lowest point (minimum) on the road.

Related terms

Critical Points: These are the points where the derivative of a function equals zero or does not exist.

Local Extrema: These are the maximum and minimum points of a function within a specific interval.

Increasing/Decreasing Intervals: These are intervals where the function is either always increasing or always decreasing.



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© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.