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 Differentiation for Graph Sketching. It falls under Calculus 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 limits, continuity, differentiability, differentiation, and anti-differentiation.
application of differentiation to graph sketching and identification of key features of graphs, including stationary points and points of inflection, and intervals over which a function is strictly increasing or strictly decreasing
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