A necessary condition for a one-variable decision problem with an objective function, which is continuous, is that the first derivative of the function be 0 at a local maximum or minimum point.

Question

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For a function to have a local maximum or minimum, the first derivative (representing the slope of the function) must be 0 at that point, indicating a change in the direction of the slope or a stationary point. This is a fundamental principle in calculus for identifying potential extremum points in continuous functions.

A Necessary Condition for a One-Variable Decision Problem with an Objective