A bicyclist is competing in a tournament. He is currently in a very hilly part of the tournament's course. For his current hill, his height in metres over time in minutes is modelled by the function;
a) Estimate the bicyclists instantaneous rate of change after 100 minutes. Round your answer to two decimal places.
b) Is the bicyclist travelling uphill or downhill at this time? Explain how you know.

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  1. hey - do you mean height OVER (meaning divided by) time or height as a function of time?

    If the latter, we need to take the derivative.

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  2. I think its as a function of time

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  3. ok
    f'(x) = v(x) = .0015 x - .5825

    at x = 100
    v(x) = .15 -.5825 = -.4325 = -.43

    dh/dt is negative, going downhill :)

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