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  • Perplex
    IB Math AAHL
    /
    Differentiation
    /

    Problem Bank

    [Maximum mark: 14]

    Let ​g(x)=ekx, where ​−1<k<1.

    1. Write down an expression for

      1. ​g′(x)​

        [1]

        To earn a crown, get your answer ready before you reveal the options!

      2. ​g′′(x)​

        [1]

    Let ​g(n)​ denote the ​nth​ derivative of ​g.

    1. Write down an expression for ​g(n)(x).

      [1]

    The function ​f​ is defined by ​f(x)=g(x)+g′(x)+g′′(x)+g(3)(x)+g(4)(x)⋯​

    1. Show that ​f(x)=1−kekx​.

      [2]

    The line ​L​ is tangent to curve ​y=f(x)​ at point ​(p,2), and intercepts the ​x​-axis at ​p−4.

    1. Find the value of ​p​ giving your answer in the form ​ln(n)−ln(m), where ​n,m∈Z.

      [9]

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