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Thread: Calculus test questions

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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) $\displaystyle f'(x) = 2x + 5$

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

    $\displaystyle f(x) = x^2 + 5x + C$.


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



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

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

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

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

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


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