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  • Perplex
    IB Math AAHL
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    Differentiation
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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: 4
    1

    !

    0 / 5

    Consider the function f(x)=3x2+2x.

    Using the limit definition of the derivative, find f′(x).

    [5]
    2

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    0 / 7

    The function h is defined by

    h(x)=21​x3−x2+4x−3.
    1. Find h′(x).

      [3]
    2. Determine the gradient of the curve y=h(x) at x=2.

      [2]
    3. Determine the equation of the tangent to y=h(x) at x=2 in the form ax+by+d=0, where a,b,d∈Z.

      [2]
    3

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    0 / 5

    Consider the function

    f(x)=x2−5x+6x2+x+k​

    and the following tables of values as x approaches 3 from below.

    x

    2.500

    2.900

    2.990

    2.999

    f(x)

    13.00

    7.67

    7.06

    7.01

    1. State x→3lim​f(x).

      [1]
    2. Explain why f(3) is undefined.

      [2]
    3. Determine the value of k.

      [2]
    4

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    0 / 6

    Consider the curve defined by

    y=3x2−4x+7.
    1. Find dxdy​.

      [2]

    The point P lies on the curve with x=1.

    1. Find the gradient of the tangent line at P.

      [1]
    2. Hence determine the equation of the normal to the curve at P in the form y=mx+c.

      [3]
    5

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