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Quadratic Ratio

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From this investigation, it can be concluded that a quartic with two distinct inflection points, whether it be a stationary point of inflection or non-stationary point of infection has a ratio of area 1:1/2:1/2:8.

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22 Pages Essays / Projects 1-2 Years old
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Topics this document covers:
Mathematics Mathematical analysis Differential calculus Analysis Analytic geometry Functions and mappings Equations Quartic function Derivative Tangent Inflection point Second derivative
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Topics this document covers:
Mathematics Mathematical analysis Differential calculus Analysis Analytic geometry Functions and mappings Equations Quartic function Derivative Tangent Inflection point Second derivative
Sample Text:
1 below. Graph 1.1: f(x) = x4 − 3x3 + 4x − 1 The aim of this investigation is to investigate the properties of a quartic polynomial, and ultimately the area ratios of a quartic function in the form A:B:C:D where areas A,B,C, D are as shown in the following graph 1.2 below. Graph 1.2: This investigation will begin with exploring a simple form of quartic and finding its area ratios by finding points of inflection Q/R and creating an equation through those points; which cut the graph again at points P/S, then creating a tangent at Q which would cut the graph again a M, then using this information creating four areas to find the area ratio of a quartic. This will be done again for a different function so a conjecture can be created, aft...
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