Relative Maximum
Definition
A relative maximum is a point on a graph where the function reaches its highest value within a specific interval. It is higher than all nearby points but may not be the absolute highest point on the entire graph.
Analogy
Think of being at an amusement park and going up and down roller coasters. A relative maximum can be compared to reaching one of those high peaks during your ride. It's higher than any other part of that particular coaster, but there might still be taller peaks elsewhere in different rides.
Related terms
Absolute Maximum: The absolute maximum is the highest point on an entire graph or function.
Critical Point: A critical point is where the derivative of a function equals zero or does not exist.
Local Maximum: A local maximum refers to the highest point within a small neighborhood around it, which may or may not be higher than other points outside that neighborhood.
"Relative Maximum" appears in:
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Additional resources (1)
Practice Questions (3)
The Second Derivative Test is used to analyze the concavity of a function and determine whether a critical point is a relative minimum, relative maximum, or neither. This test is based on the principle that:
The Second Derivative Test is a valuable tool for determining extrema because it allows us to analyze the concavity of a function at critical points. By examining the sign of the second derivative, we can identify whether a critical point corresponds to a relative minimum, relative maximum, or what else?
Where does a relative maximum of a function occur?
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