MATH 1013 Lecture Notes - Intermediate Value Theorem, Maxima And Minima, Differentiation Rules
8 Dec 2013
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Now we know differentiation rules, we can pursue better applications. How derivative affect the graph of f(x), to locate max and mins. If there is 2 points connected by a function, and it has one point above a horizontal line, and another below, then it must cross that line! Absolute maximum: if f(d) >= f(x) for all x in the domain of f, where f(d) is called the maximum value of f on the domain. Absolute minimum: if f(a) <= f(x) in all x in the domain of f, where f(a) is called the minimum value of f on the domain. Local maximum: the largest values of a certain interval. For interval (a,c) - f(b) is the local maximum in f(x), where x is sufficiently close to b. Local minimum: the smallest values of a certain interval. For interval (b,d) - f(c) is the local minimum in f(x). Since f(c) <= f(x) where x is sufficiently close to c.
