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15 March, 21:10

Describe the rate of change of f (x) = lnx. Your answer should explain how the slope changes when x is small and when x is large.

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  1. 15 March, 21:57
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    Explanation shown below

    Step-by-step explanation:

    f (x) = lnx;

    The rate of change is defined as dy/dx;

    dy/dx[Inx] = 1/x

    and dy/dx is defined as the slope

    The nature of the slope is as x increases; the slope decreases and conversely meaning as x decreases, the slope increases.
  2. 16 March, 00:53
    0
    By plotting the graph of f (x) = lnx, you can conclude that when x is small, dy/dx has a larger value. For instance, the gradient of the curve when x=0.5 is 2. However, as you move along the x axis, you will see that the graph levels off, indicating a decrease in the slope, or dy/dx. For example, if x=10, dy/dx = 0.1 and when x=20, dy/dx = 0.05 and so on. Eventually, when x is large enough the value of dy/dx will be negligible.

    Thus, as x increases, the slope decreases.
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