// Numbas version: exam_results_page_options {"name": "Differentiation: coordinates of stationary points from a graph", "extensions": ["geogebra", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"plotgraph": {"language": "javascript", "parameters": [["a", "number"], ["b", "number"], ["c", "number"], ["d", "number"]], "definition": "// This functions plots a cubic with coefficients a,b,c,d\n// It creates the board, sets it up, then returns an\n// HTML div tag containing the board.\n\n\n// Max and min x and y values for the axis.\nvar x_min = -6;\nvar x_max = 6;\nvar y_min = -10;\nvar y_max = 10;\n\n\n// First, make the JSXGraph board.\nvar div = Numbas.extensions.jsxgraph.makeBoard(\n '500px',\n '600px',\n {\n boundingBox: [x_min,y_max,x_max,y_min],\n axis: false,\n showNavigation: true,\n grid: true\n }\n);\n\n\n\n\n// div.board is the object created by JSXGraph, which you use to \n// manipulate elements\nvar board = div.board; \n\n// create the x-axis.\nvar xaxis = board.create('line',[[0,0],[1,0]], { strokeColor: 'black', fixed: true});\nvar xticks = board.create('ticks',[xaxis,1],{\n drawLabels: true,\n label: {offset: [-4, -10]},\n minorTicks: 0\n});\n\n// create the y-axis\nvar yaxis = board.create('line',[[0,0],[0,1]], { strokeColor: 'black', fixed: true });\nvar yticks = board.create('ticks',[yaxis,1],{\ndrawLabels: true,\nlabel: {offset: [-20, 0]},\nminorTicks: 0\n});\n\n\n\n\n// Plot the function.\n board.create('functiongraph',\n [function(x){ return a*x*x*x+b*x*x+c*x + d;},x_min,x_max]);\n\n\n\n\nreturn div;", "type": "html"}}, "variablesTest": {"condition": "max(abs(ymin),abs(ymax))<10", "maxRuns": 100}, "metadata": {"description": "

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.

{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]])

", "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})\$.

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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})\$.

", "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/"}]}