Example 3-7-3 - Maple Help

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Chapter 3: Applications of Differentiation

Section 3.7: What Derivatives Reveal about Graphs

Example 3.7.3

Graph fx=x610x515x4+140x3+160x2528x800 for x4,11; then use the tools of the calculus to analyze the features of this graph.

Although f is a polynomial, it presents two distinct problems. First, it is of degree six, so neither f=0 nor f=0 will have exact solutions. Moreover, even though f=0 has exact solutions, they would most likely be so cumbersome as to be useless. Hence, the analysis of the graph has to be based on numeric calculations. Second, f is very large in the specified domain, so in any reasonably sized graph the relevant features where f is not large will be "swamped" by the region where this magnitude is large. Hence, the domain must be divided accordingly when analyzing the features of the required graph.


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