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Math Help - Calculus problem

  1. #1
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    Calculus problem

    A bicyclist is riding on a path modeled by the function f(x) = 0.04(8x -x^2), where x and f(x) are measured in miles. Find the rate of change of elevation when x = 2.

    f(x) = 0.04(8x-x^2)

    The solution manual I looking over says the answer is slope of tangent line at x = 2 is rate of change, and equals about 0.16.

    I have no idea how this is about 0.16, so if anyone could shed some light it would be greatly appreciated.
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  2. #2
    MHF Contributor
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    Hi

    The change of elevation is the slope of the tangent at x=2
    In other words it is the value of the derivative at x=2

    f(x) = 0.04(8x-x^2)

    f'(x) = 0.04(8-2x)

    f'(2) = 0.04 \times 4 = 0.16
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  3. #3
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    y'=0.04(8-2x)
    =0.04(4)
    =0.16
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  4. #4
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    We haven't learned derivatives in class yet, is there another way this problem can be solved.
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  5. #5
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    You can use an approach like \frac{f(2.01)-f(2)}{0.01}
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