If f (. c) ≤ f (x) for every x in the domain of f, then the point (c, f (. c)) is a local minimum.
To determine if the point (c, f(c)) is a local minimum, we need to understand the concept of local extrema
To determine if the point (c, f(c)) is a local minimum, we need to understand the concept of local extrema. A local minimum occurs when the value of a function at a certain point is less than or equal to the values of the function at points in its immediate vicinity.
Given the statement “f(c) ≤ f(x) for every x in the domain of f”, we can infer that at the point (c, f(c)), the value of the function f(c) is less than or equal to the values of the function at all other points in its domain. This implies that there are no points in the immediate vicinity of (c, f(c)) where the function takes on a smaller value.
Therefore, based on the given information, we can conclude that the point (c, f(c)) is indeed a local minimum of the function f.
More Answers:
Understanding the Extreme Value Theorem: Exploring Absolute Maximum and Minimum Values on Closed IntervalsExploring the Intermediate Value Theorem: Understanding Continuity and Behavior of Functions
Understanding Rolle’s Theorem: Exploring the Behavior of Functions and the Existence of Zero Derivatives on Closed Intervals
Error 403 The request cannot be completed because you have exceeded your quota. : quotaExceeded