What is an increasing function?
Increasing/Decreasing

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•
Mathematics
•
9th - 12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
A function is increasing on an interval if, for any two points in that interval, the function value at the second point is greater than the function value at the first point.
2.
FLASHCARD QUESTION
Front
What is a decreasing function?
Back
A function is decreasing on an interval if, for any two points in that interval, the function value at the second point is less than the function value at the first point.
3.
FLASHCARD QUESTION
Front
How do you determine the increasing interval of a function?
Back
To determine the increasing interval, find where the derivative of the function is positive.
4.
FLASHCARD QUESTION
Front
How do you determine the decreasing interval of a function?
Back
To determine the decreasing interval, find where the derivative of the function is negative.
5.
FLASHCARD QUESTION
Front
What does it mean if a function is constant on an interval?
Back
A function is constant on an interval if it does not change value; its derivative is zero on that interval.
6.
FLASHCARD QUESTION
Front
What is the significance of critical points in determining increasing/decreasing intervals?
Back
Critical points are where the derivative is zero or undefined; they help identify potential intervals of increase or decrease.
7.
FLASHCARD QUESTION
Front
What is the first derivative test?
Back
The first derivative test is a method to determine whether a critical point is a local maximum, local minimum, or neither by analyzing the sign of the derivative before and after the point.
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