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    Hi would really appreciate it if anyone could please explain an easy way how to draw a derived graph. I know that the points you plot are the are the roots(stationary points) but I do not know which way to draw the lines as I find it confusing to visualise when it is a positive direction etc it just doesn't make sense

    Once you have figured out the coordinates turning points, look at the derived equation of the graph. Stationary points is the x coordinate of the turning point of the original graph (also known as the roots).
    If the derived equation is something like 3x²+ 6x +9, and the original equation was x³ + 3x²+ 9x - 15, the part on the original graph that would be increasing would be above the x-axis on the derived graph. The part on the original graph that would be decreasing would be below the x-axis of the derived graph.
    For example, if the line on the original graph is increasing, on the derived graph the line would be above the x - axis going towards your first stationary point. When the line reaches the turning point on the original graph, it turn round and decreases. On the derived graph, the line will go below the x -axis. Once the original graph turns round on its second turning point so it is increasing, the line on the derived graph will go through the second stationary point so the line is above the x-axis.

    I am not really good at explaining things, so I hope you understood all of the above. If not, just ask and I will try and explain it as best as I can.
    Also, sorry this post is kind of late seeing as the maths exam is tomorrow. But I only saw it a few minutes ago - well like an hour now after some editing...
    So I wish you the best of luck for tomorrow, and I hope this helped.
    Good Luck!!!!:cute::thumbsup:
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