{plotgraph(a,b,c,d)}

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Above is the graph of some function \$f\$.

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What are the coordinates of its maximum point? ([[0]],[[1]])

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What are the coordinates of its minimum point? ([[2]],[[3]])

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A cubic with a maximum and minimum point is given. Question is to determine coordinates of the minimum and maximum point. Non-calculator. Advice is given.

"}, "type": "question", "statement": "

Finding stationary points on a graph.

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(i) A maximum point is a point where regardless if you move right or left, the height will decrease.  A visual analogy would be a hill: if you're at the top of a hill, no matter which direction you go your height will decrease.  So you're looking for a part of the graph which is 'like a hill', and in this graph the point is at \$(\\var{xmax}, \\var{ymax})\$.

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(ii) A minimum point is the opposite of a maximum point (or an upside-down version of a maximum point, if you like).  The analogy in this case would be a valley: no matter which direction you go your height will increase.  In this graph, the minimum point is at \$(\\var{xmin}, \\var{ymin})\$.

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