Extrema
Flashcard
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Mathematics
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Practice Problem
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Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is an extremum?
Back
An extremum is a point in a function where the function reaches a local maximum or minimum value.
2.
FLASHCARD QUESTION
Front
What is the difference between relative and absolute extrema?
Back
Relative extrema are the highest or lowest points in a specific interval, while absolute extrema are the highest or lowest points over the entire domain of the function.
3.
FLASHCARD QUESTION
Front
How do you find relative maxima and minima?
Back
To find relative maxima and minima, take the derivative of the function, set it to zero, and solve for critical points. Then, use the second derivative test or the first derivative test to classify these points.
4.
FLASHCARD QUESTION
Front
What is the first derivative test?
Back
The first derivative test involves analyzing the sign of the derivative before and after a critical point to determine if it is a maximum or minimum.
5.
FLASHCARD QUESTION
Front
What is the second derivative test?
Back
The second derivative test uses the second derivative of a function to determine the concavity at a critical point. If the second derivative is positive, the point is a local minimum; if negative, it is a local maximum.
Tags
CCSS.HSF.IF.A.2
6.
FLASHCARD QUESTION
Front
What is a global (absolute) maximum?
Back
A global maximum is the highest point over the entire domain of a function.
7.
FLASHCARD QUESTION
Front
What is a global (absolute) minimum?
Back
A global minimum is the lowest point over the entire domain of a function.
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