Example 3-7-3 - Maple Help



Chapter 3: Applications of Differentiation



Section 3.7: What Derivatives Reveal about Graphs



Example 3.7.3



 Graph $f\left(x\right)={x}^{6}-10{x}^{5}-15{x}^{4}+140{x}^{3}+160{x}^{2}-528x-800$ for $x\in \left[-4,11\right]$; 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 $f\prime =0$ 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, $\left|f\right|$ is very large in the specified domain, so in any reasonably sized graph the relevant features where $\left|f\right|$ 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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