A new theme park is designing a rollercoaster. The height of the rollercoaster above the ground is modelled by a polynomial function, $h(x)$, where $x$ is the horizontal distance from the starting point of the rollercoaster, and $h(x)$ is the height in meters. The section of the rollercoaster between $x=0$ and $x=8$ is modelled by a quartic polynomial. It is known that the rollercoaster starts at ground level, has a local minimum at $(2, -4)$, and returns to ground level at $x=8$. Additionally, there is a point of inflection at $x=5$.
c. Analyse the behavior of $h’(x)$ around $x=5$ to demonstrate that $x=5$ is indeed a point of inflection, assuming $h(x)$ as derived in parts (a) and (b).
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 3 marks, testing your understanding of Polynomial Function Graphs. It falls under Functions, relations and graphs in Unit 3: Mathematical Methods Unit 3. Submit your answer above to receive instant AI-powered marking and personalised feedback.
Extend introductory study of functions, algebra, calculus. Focus on functions, relations, graphs, algebra, and applications of derivatives.
Covers transformations, polynomial functions, power functions, exponential functions, logarithmic functions, circular functions, and combinations of these.
graphs of polynomial functions and their key features
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