The Horrible Hotel is a theme park attraction with an elevator that raises and drops at high speeds. The function below gives the height of the elevator in metres as a function of time t in seconds for a part of the ride, f(t) = 2t3 – 6t2 + 20. (a) Plot a graph of the function over the interval –1

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Chapter5: Polynomial And Rational Functions
Section5.1: Quardratic Functions
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The Horrible Hotel is a theme park attraction with an elevator that raises and drops at high speeds.
The function below gives the height of the elevator in metres as a function of time t in seconds for
a part of the ride,
f(t) = 2t3 – 6t2 + 20.
(a) Plot a graph of the function over the interval –1 <t< 3.
(b) A survey indicated that guests were most exhilarated when the elevator changed between
moving upwards and downwards. Use the graph to find the times that this occurs, i.e. give the
points where the tangent line to the graph is horizontal.
(c) Use the limit definition of the derivative at a point to show that the derivative of the function
is zero at these points.
Transcribed Image Text:The Horrible Hotel is a theme park attraction with an elevator that raises and drops at high speeds. The function below gives the height of the elevator in metres as a function of time t in seconds for a part of the ride, f(t) = 2t3 – 6t2 + 20. (a) Plot a graph of the function over the interval –1 <t< 3. (b) A survey indicated that guests were most exhilarated when the elevator changed between moving upwards and downwards. Use the graph to find the times that this occurs, i.e. give the points where the tangent line to the graph is horizontal. (c) Use the limit definition of the derivative at a point to show that the derivative of the function is zero at these points.
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