How Do We Know the Shape of a Function?

Thomas J. Pfaff ()
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Thomas J. Pfaff: Ithaca College, Department of Mathematics

Chapter Chapter 17 in Applied Calculus with R, 2023, pp 211-226 from Springer

Abstract: Abstract Consider the graph of $$f(x)=x^3-3003x^2+3006000x$$ f ( x ) = x 3 - 3003 x 2 + 3006000 x in figure 17.1. Can we conclude the function does not have any local maximums, local minimums, or inflection points? If we think we do not have the correct window (domain and range of the graph) how do we decide what window to use? In this chapter we will use the derivative, both the first and second, to completely understand the shape of a graph.

Date: 2023
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DOI: 10.1007/978-3-031-28571-4_17

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