Relative Minimum
Definition
A relative minimum is a point on a graph where the function reaches its lowest value within a specific interval. It is lower than all nearby points but may not be the absolute lowest point on the entire graph.
Related terms
Absolute Minimum: The absolute minimum is the lowest 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 Minimum: A local minimum refers to the lowest point within a small neighborhood around it, which may or may not be lower than other points outside that neighborhood.
"Relative Minimum" appears in:
Study guides (2)
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 minimum of a function occur?
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