AP Calculus AB Flashcards: Using the First Derivative Test to Determine Relative (Local) Extrema
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 10 cards to help you master important concepts.
What kind of information can be found by analyzing a function's first derivative?
Analyzing the first derivative can determine the location of the function's relative (local) extrema.
Card 1 of 10
All Flashcards (10)
What kind of information can be found by analyzing a function's first derivative?
Analyzing the first derivative can determine the location of the function's relative (local) extrema.
Based on the provided text, what is a "relative (local) extremum"?
It is a feature of a function whose location can be determined by analyzing the behavior of the first derivative.
Define the utility of the first derivative in the context of finding extrema.
The first derivative's utility is in determining the location of a function's relative (local) extrema.
You need to justify your finding of a relative extremum for a function f(x). What must you base your justification on?
The justification must be based on the behavior of the function's derivatives.
What primary tool is used to find the location of a function's relative (local) extrema?
The first derivative of the function is used to determine the location of its relative (local) extrema.
What is the fundamental principle for making a defensible claim about a function's behavior?
The principle is that conclusions about the behavior of a function must be justified based on the behavior of its derivatives.
What is the relationship between the behavior of a function's derivatives and the function itself?
The behavior of a function's derivatives can be used to justify conclusions about the behavior of the function.
If a calculus problem asks you to find and justify all relative extrema, what specific tool does this topic suggest you use?
This topic suggests using the first derivative to determine the location of the relative (local) extrema and justify the conclusion.
What provides the evidence needed to support conclusions about a function's behavior?
The behavior of the function's derivatives provides the evidence needed to justify conclusions about the function's behavior.
A student has found the critical points of a function. What is the next step in determining which of these are relative extrema?
The next step is to analyze the behavior of the function's first derivative around those points to justify conclusions about relative extrema.