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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.
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\nAbove is the graph of some function $f$.
\nWhat are the coordinates of its maximum point? ([[0]],[[1]])
\nWhat are the coordinates of its minimum point? ([[2]],[[3]])
", "showFeedbackIcon": true, "scripts": {}, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "variableReplacementStrategy": "originalfirst"}], "tags": [], "advice": "(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 $(\\var{xmax}, \\var{ymax})$.
\n(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 $(\\var{xmin}, \\var{ymin})$.
", "statement": "Finding stationary points on a graph.
", "name": "Differentiation: coordinates of stationary points from a graph", "type": "question", "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}]}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}