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Math Help - Calculus test questions

  1. #1
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    Calculus test questions

    1) The curve with equation y=f(x) passes through the point (3,-1) and f '(x)=2x+5. find f(x).




    2) find s in terms of t, if ds/dt=t+3-1/t^2 and s=6 and t=1.
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  2. #2
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    1) f'(x) = 2x + 5

    f(x) = \int{2x + 5\,dx}

    f(x) = x^2 + 5x + C.


    You know that the point (3, -1) lies on the curve, so substitute it in and solve for C.



    2) \frac{ds}{dt} = t + 3 - \frac{1}{t^2}

    \frac{ds}{dt} = t + 3 - t^{-2}

    s = \int{t + 3 - t^{-2}\,dt}

    s = \frac{t^2}{2} + 3t - \frac{t^{-1}}{-1} + C

    s = \frac{t^2}{2} + 3t + \frac{1}{t} + C.


    Now substitute s = 6 and t = 1 to find C.
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