Absolute Extrema
Definition
The absolute extrema of a function are the highest and lowest values that the function reaches over a given interval.
Analogy
Think of a roller coaster ride. The highest point on the roller coaster represents the absolute maximum, while the lowest point represents the absolute minimum.
Related terms
Local Extrema: These are points where a function reaches its highest or lowest value within a small neighborhood, but not necessarily over an entire interval.
Critical Points: These are points where the derivative of a function is either zero or undefined. They can help identify potential extrema.
Global Extrema: These are the absolute maximum and minimum values of a function over its entire domain.
"Absolute Extrema" appears in:
Study guides (2)
Additional resources (2)
Practice Questions (5)
What do absolute extrema represent?
What is the difference between relative extrema and absolute extrema?
Which test is useful for determining the absolute extrema of a function over its domain?
How do you determine the absolute extrema using the Candidates Test?
Consider the function f(x) = x^2. Which statement about the absolute extrema is correct?
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