A graph that is large enough to show a functions global

Chapter , Problem 13

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A graph that is large enough to show a functions global behavior may fail to reveal important local features. The graph of is a case in point. a. Graph over the interval Where does the graph appear to have local extreme values or points of inflection? b. Now factor and show that has a local maximum at and local minima at c. Zoom in on the graph to find a viewing window that shows the presence of the extreme values at and The moral here is that without calculus the existence of two of the three extreme values would probably have gone unnoticed. On any normal graph of the function, the values would lie close enough together to fall within the dimensions of a single pixel on the screen. (Source: Uses of Technology in the Mathematics Curriculum, by Benny Evans and Jerry Johnson, Oklahoma State University, published in 1990 under National Science Foundation Grant USE-8950044.)