How to distinguish a peak from a valley in calculus
In short: Finding a critical point is only half the battle. This video explains how to determine whether that point represents a relative maximum, a relative minimum, or neither by analyzing the behavior of the first derivative.
The first derivative test provides a systematic way to classify critical points. By examining how the sign of the derivative changes as you move across a point, you can identify the shape of the function's curve.
This method is a foundational component of AP Calculus AB, designed to help students transition from identifying where a function stops changing to understanding the nature of that change.
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Sources
- Summary by Intellect · source: Finding relative extrema (first derivative test) | AP Calculus AB | Khan Academy
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