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  • Perplex
    IB Math AIHL
    /
    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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    23 / 78 problems visible - Upgrade to view all problems

    IB: 6
    45

    0 / 16

    The graph y=f(x) of the function f(x)=p2x4−px3+qx2+px+q, where p,q>0, is concave up over its entire domain.

    1. Show that q>83​.

      [6]

    The line L has slope p and x-intercept −23​. It is given that L is tangent to the curve of y=f(x).

    1. Show that q=23p​.

      [5]
    2. Given that f′′(p1​)=5f′(0), find the value of p and the value of q.

      [5]
    46

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    Consider the line L with slope −m, where m>0, passing through the point (3,5).

    1. Give an expression in terms of m for

      (i) the x-intercept of the line,

      (ii) the y-intercept of the line.

      [5]

    The line L forms a triangle with the coordinate axes.

    1. Show that the area of this triangle is A=2m9m2+30m+25​.

      [2]
    2. Find the minimum possible area of the triangle.

      [5]
    47

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    48

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    49

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    51

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    52

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    53

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