Extrema and Increasing Decreasing Intervals
Flashcard
•
Mathematics
•
11th Grade
•
Practice Problem
•
Hard
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15 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) is rising as x increases.
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) is falling as x increases.
3.
FLASHCARD QUESTION
Front
How do you determine increasing and decreasing intervals from a graph?
Back
By analyzing the slope of the tangent line: if the slope is positive, the function is increasing; if negative, it is decreasing.
4.
FLASHCARD QUESTION
Front
What is an extremum in calculus?
Back
An extremum is a point in a function where it reaches a local maximum or minimum value.
5.
FLASHCARD QUESTION
Front
What is the difference between local maximum and local minimum?
Back
A local maximum is the highest point in a neighborhood, while a local minimum is the lowest point in a neighborhood.
6.
FLASHCARD QUESTION
Front
How can you find extrema using the first derivative test?
Back
By finding critical points where the first derivative is zero or undefined, and then testing intervals around these points.
7.
FLASHCARD QUESTION
Front
What does it mean if a function has no extrema?
Back
It means the function does not have any local maximum or minimum points within the given interval.
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