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  • Perplex
    IB Math AISL
    /
    Differentiation
    /

    Problems

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    Problem Bank - Differentiation

    Access custom-built, exam-style problems for differentiation. Each problem has a full solution and mark-scheme, as well as AI grading and support.

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    IB: 6
    16

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    Patrick has a 5cm×8cm rectangular piece of cardboard. He is making an open-top box by cutting equal squares of side length h from each corner of the sheet, and then folding up the sides.

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    1. Find an expression for the volume of the box V(h).

      [3]
    2. Find an expression for V′(h).

      [1]
    3. Hence, find the value of h that maximizes V

      [4]
    17

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    Consider two curves defined by

    y=f(x)=x3+2andy=g(x)=4x2−4x+2.
    1. Find f′(x) and g′(x).

      [2]
    2. Solve f′(x)=g′(x).

      [2]
    3. State the values of x at which the two curves touch.

      [2]
    4. Find the equation of their common tangent line in the form y=mx+c.

      [3]
    18

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