AP Calculus AB Flashcards: Using the Candidates Test to Determine Absolute (Global) 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.
A student finds a critical point for a function f(x) at x=10. If they are looking for absolute extrema on the interval [0, 8], what should they do with this critical point?
The student should disregard the critical point at x=10 because it is outside the closed interval [0, 8], and only test the endpoints and any critical points within the interval.
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A student finds a critical point for a function f(x) at x=10. If they are looking for absolute extrema on the interval [0, 8], what should they do with this critical point?
The student should disregard the critical point at x=10 because it is outside the closed interval [0, 8], and only test the endpoints and any critical points within the interval.
What is the final step of the Candidates Test to determine which candidate is the absolute maximum?
After identifying all candidates (endpoints and interior critical points), you must evaluate the function at each candidate and identify the largest resulting value.
If a function has no critical points within a closed interval [a, b], where must its absolute extrema be located?
If there are no critical points within the interval, the absolute maximum and minimum must occur at the endpoints, x=a and x=b.
How does the behavior of a function's derivatives help in finding absolute extrema?
Analyzing a function's derivatives allows us to identify its critical points, which are necessary candidates to test for absolute extrema along with the interval's endpoints.
How does finding a function's critical points relate to justifying conclusions about its behavior?
Finding critical points by analyzing derivatives is the first step in justifying conclusions about a function's local and potential absolute extrema.
What is a critical point?
A critical point is a point in the interior of a function's domain where its derivative is either zero or undefined; these are potential locations for extrema.
According to the Candidates Test, where can the absolute (global) extrema of a function on a closed interval occur?
The absolute (global) extrema of a function on a closed interval can only occur at the function's critical points or at the endpoints of the interval.
What are the 'candidates' when using the Candidates Test for absolute extrema?
The candidates are the function's critical points located within the closed interval and the endpoints of that interval.
To find the absolute minimum of a continuous function on the interval [0, 5], what specific locations must be evaluated?
You must evaluate the function at the endpoints (x=0 and x=5) and at all critical points that lie within the closed interval [0, 5].
What is the core justification for limiting the search for absolute extrema to only critical points and endpoints on a closed interval?
This method is justified because an extremum must occur either where the function's rate of change is zero or undefined (a critical point) or at the boundary of the interval.