
Increasing, Decreasing, Positive, and Negative Intervals
Flashcard
•
Mathematics
•
11th Grade
•
Practice Problem
•
Hard
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14 questions
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1.
FLASHCARD QUESTION
Front
What is an increasing interval in a function?
Back
An increasing interval is a range of x-values where the function's output (y-values) rises as x increases. For example, if f(x) is increasing on the interval (1, 3), then f(1) < f(2) < f(3).
2.
FLASHCARD QUESTION
Front
What is a decreasing interval in a function?
Back
A decreasing interval is a range of x-values where the function's output (y-values) falls as x increases. For example, if f(x) is decreasing on the interval (3, 5), then f(3) > f(4) > f(5).
3.
FLASHCARD QUESTION
Front
Define positive interval in the context of a function.
Back
A positive interval is a range of x-values where the function's output (y-values) is greater than zero. For example, if f(x) is positive on the interval (0, 2), then f(x) > 0 for all x in (0, 2).
4.
FLASHCARD QUESTION
Front
Define negative interval in the context of a function.
Back
A negative interval is a range of x-values where the function's output (y-values) is less than zero. For example, if f(x) is negative on the interval (-2, 0), then f(x) < 0 for all x in (-2, 0).
5.
FLASHCARD QUESTION
Front
How can you determine increasing and decreasing intervals from a graph?
Back
To determine increasing and decreasing intervals from a graph, observe the slope of the curve. If the curve rises as you move from left to right, it is increasing; if it falls, it is decreasing.
6.
FLASHCARD QUESTION
Front
What is the first derivative test?
Back
The first derivative test is a method used to determine the local maxima and minima of a function by analyzing the sign of the first derivative. If f'(x) changes from positive to negative at a point, that point is a local maximum.
7.
FLASHCARD QUESTION
Front
What does it mean if a function is constant on an interval?
Back
If a function is constant on an interval, it means that the output (y-values) does not change as the input (x-values) varies. For example, f(x) = 5 is constant for all x.
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