An engineer is designing a roller coaster for younger children and has tried some functions to model the height of the roller coaster during the first 300 yards. She came up with the following function to describe what she believes would make a fun start to the ride: $H(x) = -3x^4 + 21x^3 - 48x^2 + 36x$, where $H(x)$ is the height of the roller coaster (in yards) when the roller coaster is 100$x$ yards from the beginning of the ride. Answer the following questions to help determine at which distances from the beginning of the ride the roller coaster is at its lowest height. g. How do you think the engineer came up with the function for this model?
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The engineer likely started by considering the shape of a roller coaster. Roller coasters typically have a peak and then descend, so the engineer would want to model a function that starts high and then decreases. Show more…
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