5.8 Stationary points, optimisation and inflexion

5.8 Stationary points, optimisation and inflexion Quiz

IB Maths: Analysis and Approaches HL: Quiz

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  1. 1. f(x)=x2−8x+3f(x)=x^{2}-8x+3. Find the coordinates of the stationary point.

    • A. (4, −13)(4,\,-13)
    • B. (−4, 51)(-4,\,51)
    • C. (4, 3)(4,\,3)
    • D. (8, 3)(8,\,3)

  2. 2. At a stationary point f′′(a)=−5f''(a)=-5. The point is

    • A. a local minimum
    • B. a local maximum
    • C. a point of inflexion
    • D. impossible to classify

  3. 3. For f(x)=x3−3x2f(x)=x^{3}-3x^{2}, where is the point of inflexion?

    • A. x=0x=0
    • B. x=2x=2
    • C. x=1x=1
    • D. x=3x=3

  4. 4. The graph of y=x4y=x^{4} at x=0x=0 has

    • A. a point of inflexion
    • B. a local maximum
    • C. a local minimum
    • D. a non-stationary point

  5. 5. A rectangle has perimeter 20 cm. What is its greatest possible area?

    • A. 2020 cm2^{2}
    • B. 2424 cm2^{2}
    • C. 100100 cm2^{2}
    • D. 2525 cm2^{2}

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