What is the definition of a local extremum?
Calc Extrema

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•
Mathematics
•
11th - 12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
A local extremum is a point in the domain of a function where the function takes on a maximum or minimum value relative to its immediate surroundings.
2.
FLASHCARD QUESTION
Front
What does it mean for a function to be increasing?
Back
A function f(x) is increasing on an interval if for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) < f(x2).
3.
FLASHCARD QUESTION
Front
What is the relationship between f(x) and f'(x) regarding increasing and decreasing intervals?
Back
If f'(x) > 0, then f(x) is increasing. If f'(x) < 0, then f(x) is decreasing.
4.
FLASHCARD QUESTION
Front
How do you determine the intervals where a function is increasing or decreasing using a sign chart?
Back
A sign chart shows the sign of f'(x) over different intervals. Positive values indicate increasing intervals, while negative values indicate decreasing intervals.
5.
FLASHCARD QUESTION
Front
What is a critical point?
Back
A critical point occurs where f'(x) = 0 or where f'(x) is undefined. These points are potential locations for local extrema.
6.
FLASHCARD QUESTION
Front
What is the first derivative test?
Back
The first derivative test is a method used to determine whether a critical point is a local maximum, local minimum, or neither by analyzing the sign of f'(x) before and after the critical point.
7.
FLASHCARD QUESTION
Front
What is a local maximum?
Back
A local maximum is a point where the function value is greater than the values of the function at nearby points.
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