5.7 The second derivative

5.7 The second derivative Quiz

IB Maths: Analysis and Approaches HL: Quiz

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5 questions, one answer each

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  1. 1. Find f′′(x)f''(x) when f(x)=2x3−x2+7xf(x)=2x^{3}-x^{2}+7x.

    • A. 6x2−2x+76x^{2}-2x+7
    • B. 12x−212x-2
    • C. 12x12x
    • D. 6x−26x-2

  2. 2. Find d2ydx2\dfrac{d^{2}y}{dx^{2}} when y=e−2xy=e^{-2x}.

    • A. −2e−2x-2e^{-2x}
    • B. 4e−2x4e^{-2x}
    • C. −4e−2x-4e^{-2x}
    • D. e−2xe^{-2x}

  3. 3. On an interval, f′(x)<0f'(x)<0 and f′′(x)>0f''(x)>0. Which describes ff?

    • A. Increasing, getting steeper
    • B. Decreasing, with the gradient increasing towards zero
    • C. Decreasing, getting steeper
    • D. Increasing, levelling off

  4. 4. Find f′′(π)f''(\pi) when f(x)=cos⁡xf(x)=\cos x.

    • A. 11
    • B. −1-1
    • C. 00
    • D. π\pi

  5. 5. The volume VV of water in a tank satisfies dVdt>0\dfrac{dV}{dt}>0 and d2Vdt2<0\dfrac{d^{2}V}{dt^{2}}<0. What is happening?

    • A. The tank is emptying faster and faster
    • B. The tank is filling more and more quickly
    • C. The tank is filling, but more and more slowly
    • D. The tank is emptying, but more and more slowly

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