MATH 140 Lecture 16: Graphing Problems Involving Derivatives

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Then f(x0) = maximum value for all x in [a, b]. for all x in [a, b]; it is the minimum if f (x) f (x0) f ( x) f (x0) if f (x0) is an extreme value if it is a maximum or a minimum value: note: an extreme value is a value of f. 1: f ( x)=1 x2 , 2 x 1 find any extrema: graph the function, according to the graph, the maximum value is 1 and the minimum is 3. 2: g(x)=x3 , 1 x 1: plug in given values: g ( 1)=( 1)3= 1 g (1)=13=1, the maximum value is 1 and the minimum is 1. 2"": k ( x)=x4 ,

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