AP Calculus BC Flashcards: Determining Intervals on Which a Function Is Increasing or Decreasing
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 is the basis for justifying conclusions about a function's behavior?
Conclusions about the behavior of a function must be justified based on the behavior of its derivatives.
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What is the basis for justifying conclusions about a function's behavior?
Conclusions about the behavior of a function must be justified based on the behavior of its derivatives.
If you are given that f'(x) < 0 on the interval (2, 5), what can you conclude about the function f(x)?
You can conclude that the function f(x) is decreasing on the interval (2, 5), as this conclusion is justified by the negative behavior of its first derivative.
First Derivative Test for Increasing/Decreasing
This test uses the sign of the first derivative to draw conclusions about the function's behavior; a positive derivative implies the function is increasing, while a negative derivative implies it is decreasing.
What is the primary calculus tool used to determine where a function is increasing or decreasing?
The first derivative of the function is the primary tool used to find information about the intervals where the function is increasing or decreasing.
To justify that a function is increasing on an interval, what must be true about its first derivative?
To justify that a function is increasing on an interval, you must show that its first derivative is positive on that interval.
If you are given that f'(x) > 0 on the interval (-1, 3), what can you conclude about the function f(x)?
You can conclude that the function f(x) is increasing on the interval (-1, 3), because the behavior of its first derivative is positive.
To justify that a function is decreasing on an interval, what must be true about its first derivative?
To justify that a function is decreasing on an interval, you must show that its first derivative is negative on that interval.
What information does the first derivative of a function provide about its graph?
The first derivative of a function provides information about the intervals where the function is increasing or decreasing.
How are a function and its derivatives connected in terms of their behavior?
The behavior of a function's derivatives can be analyzed to make and justify conclusions about the behavior of the original function, such as identifying intervals of increase or decrease.
Justification of Function Behavior
The process of using the behavior of a function's derivatives (e.g., the sign of the first derivative) to support claims about the function's own behavior (e.g., increasing or decreasing).