3.5 Intervals of increase and decrease

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Mathematics
•
9th - 12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is an interval of increase?
Back
An interval of increase is a range of x-values where the function's output (y-values) is rising as x increases.
2.
FLASHCARD QUESTION
Front
What is an interval of decrease?
Back
An interval of decrease is a range of x-values where the function's output (y-values) is falling as x increases.
3.
FLASHCARD QUESTION
Front
What does it mean for a function to be constant over an interval?
Back
A function is constant over an interval if its output (y-values) does not change as x increases within that interval.
4.
FLASHCARD QUESTION
Front
How can you identify intervals of increase and decrease on a graph?
Back
Intervals of increase are where the graph rises from left to right, and intervals of decrease are where the graph falls from left to right.
5.
FLASHCARD QUESTION
Front
What is the significance of critical points in determining intervals of increase and decrease?
Back
Critical points are where the derivative is zero or undefined; they help identify where the function changes from increasing to decreasing or vice versa.
6.
FLASHCARD QUESTION
Front
How do you determine the number of intervals in a function?
Back
Count the distinct sections of the graph where the function is either increasing, decreasing, or constant.
7.
FLASHCARD QUESTION
Front
What is the relationship between the first derivative and intervals of increase/decrease?
Back
If the first derivative is positive, the function is increasing; if negative, the function is decreasing.
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