MA 141 Study Guide - Final Guide: Constant Function, Mean Value Theorem, Maxima And Minima
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One point of interest of a given graph might be the highest or lowest values of the graph. We"d like to use the derivative to nd these values. Observe: the tangent line is horizontal at points a and b, the derivative does not appear to exist at c and d, the absolute highest point on this graph occurs at f . The y-coordinate of f is called the absolute maximum of f : the absolute lowest point on this graph occurs at b. The y-coordinate of b is called the absolute minimum of f . We use the term "extrema" to mean either maximum or minimum (extreme values). Def: let f be a function with domain d and let c d. then we say f (c) is a local maximum value of f if f (x) f (c) for all x d near c.
