A new theme park is designing a rollercoaster. The height, $h$ (in meters), of the rollercoaster track above the ground is modelled by different functions along its path. For the first section of the ride, the height is modelled by a polynomial function. For the second section, the height is modelled by a trigonometric function. Finally, for the third section, the height is modelled by an exponential function.
a. The first section of the rollercoaster is modelled by the polynomial function $h_1(x) = ax^3 + bx^2 + cx + d$, where $x$ is the horizontal distance (in meters) from the starting point of the rollercoaster and \$0 \le x \le 100$. The rollercoaster starts at ground level, has a local minimum at $x = 20$ where the height is also ground level, and reaches a height of 27 meters at $x=60$. Determine the values of $a$, $b$, $c$, and $d$.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 4 marks, testing your understanding of Modelling with Functions. 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.
modelling of practical situations using polynomial, power, circular, exponential and logarithmic functions, simple transformation and combinations of these functions, including simple piecewise (hybrid) functions.
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