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{"name": "Differentiation: coordinates of stationary points from a graph", "extensions": ["geogebra", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": [], "parts": [{"scripts": {}, "extendBaseMarkingAlgorithm": true, "type": "gapfill", "showCorrectAnswer": true, "prompt": "<p>{plotgraph(a,b,c,d)}</p>\n<p>Above is the graph of some function $f$.</p>\n<p>What are the coordinates of its maximum point? [[0]]</p>\n<p>What are the coordinates of its minimum point? [[1]]</p>", "marks": 0, "showFeedbackIcon": true, "variableReplacements": [], "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "gaps": [{"scripts": {}, "extendBaseMarkingAlgorithm": true, "numRows": 1, "type": "matrix", "showCorrectAnswer": true, "marks": "1", "variableReplacements": [], "showFeedbackIcon": true, "correctAnswer": "matrix([xmax,ymax])", "tolerance": 0, "numColumns": "2", "allowResize": false, "markPerCell": false, "correctAnswerFractions": false, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "allowFractions": false, "unitTests": []}, {"scripts": {}, "extendBaseMarkingAlgorithm": true, "numRows": 1, "type": "matrix", "showCorrectAnswer": true, "marks": "1", "variableReplacements": [], "showFeedbackIcon": true, "correctAnswer": "matrix([xmin,ymin])", "tolerance": 0, "numColumns": "2", "allowResize": false, "markPerCell": false, "correctAnswerFractions": false, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "allowFractions": false, "unitTests": []}], "customMarkingAlgorithm": "", "unitTests": []}], "preamble": {"js": "", "css": ""}, "functions": {"plotgraph": {"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;", "parameters": [["a", "number"], ["b", "number"], ["c", "number"], ["d", "number"]], "language": "javascript", "type": "html"}}, "advice": "<p>See 11.4 and 11.5 for background on stationary points.</p>", "metadata": {"description": "<p><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;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.&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:513,&quot;3&quot;:[null,0],&quot;12&quot;:0}\">A cubic with a maximum and minimum point is given. Question is to determine coordinates of the minimum and maximum point.</span></p>", "licence": "Creative Commons Attribution 4.0 International"}, "extensions": ["geogebra", "jsxgraph"], "variablesTest": {"maxRuns": 100, "condition": "max(abs(ymin),abs(ymax))<10"}, "statement": "", "rulesets": {}, "name": "Differentiation: coordinates of stationary points from a graph", "ungrouped_variables": ["a", "r1", "r2", "ymin", "ymax", "xmax", "xmin", "b", "c", "d"], "variables": {"b": {"name": "b", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "-(r1*a + 3*r2)/2"}, "xmin": {"name": "xmin", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "if(a=1, max(r1/3, r2/a), min(r1/3, r2/a))"}, "ymin": {"name": "ymin", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "a*(xmin)^3+b*(xmin)^2+c*(xmin) + d"}, "c": {"name": "c", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "r1*r2"}, "a": {"name": "a", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(-1..1 except 0)"}, "r2": {"name": "r2", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(-1..1 except 1/2*(a*r1/3 + mod(a*r1,2)))*2-mod(a*r1,2)"}, "ymax": {"name": "ymax", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "a*(xmax)^3+b*(xmax)^2+c*(xmax) + d"}, "xmax": {"name": "xmax", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "if(a=1, min(r1/3, r2/a), max(r1/3, r2/a))"}, "d": {"name": "d", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(-2..2)"}, "r1": {"name": "r1", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(-1..1)*3"}}, "variable_groups": [], "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/"}]}