Need an research paper on using differentiation find the difference between maximum and minimum heights for both the roller coasters. Needs to be 3 pages. Please no plagiarism. In the laboratory, one tries to establish cause and effect relationship of a phenomenon. Due to various objective difficulties, many relationships cannot be established through laboratory experiments. This is when the relationship is established through mathematical formulas that model a phenomenon or object. Then by changing the values of one or more variables one can get the answers needed in the real world problems.

This assignment does not report either development of a mathematical model or present a mathematical model. It uses a mathematical model to derive certain cause and effect relationship. The assignment uses two different models that describe at what height from the ground a coaster will be located at a certain period.

The model expressed by the equation h (t) = – 2 t3 + 34 t2 – 128 t + 96 describes the location of a coaster from the ground for 12 seconds after it comes out of the loop. The given equation is a third degree polynomial equation where the dependent variable is height and the independent variable is time. The scope is to determine maximum and minimum heights from the ground level. The maximum and minimum will be found through the derivatives of the equation. The condition for maximum is h’ (t) = 0, and h” (t) is negative. The condition of minimum is h’ (t) = 0, and h” (t) is positive (Lawrence Spector n.d.).

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