Chapter 4 | Applications of Derivatives
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Figure 4.20 This function has an absolute maximum at an endpoint of the interval.
Find the absolute maximum and absolute minimum of f ( x ) = x 2 −4 x +3 over the interval [1, 4].
4.13
At this point, we know how to locate absolute extrema for continuous functions over closed intervals. We have also defined local extrema and determined that if a function f has a local extremum at a point c , then c must be a critical point of f . However, c being a critical point is not a sufficient condition for f to have a local extremum at c . Later in this chapter, we show how to determine whether a function actually has a local extremum at a critical point. First, however, we need to introduce the Mean Value Theorem, which will help as we analyze the behavior of the graph of a function.
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