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.
Analogy
Imagine you are hiking up and down hills in a forest. A relative minimum is like reaching the bottom of a small valley before climbing up another hill. It's the lowest point in that particular section, but there might be even lower valleys elsewhere.
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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