// Numbas version: exam_results_page_options
{"name": "Partial differentiation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "c", "ch", "d", "m", "s5", "a1", "other", "b1", "c2", "c1", "b", "check", "d1"], "name": "Partial differentiation", "variablesTest": {"maxRuns": 100, "condition": ""}, "variable_groups": [], "parts": [{"showFeedbackIcon": true, "scripts": {}, "gaps": [{"checkingAccuracy": 0.001, "showFeedbackIcon": true, "expectedVariableNames": ["x", "y"], "answer": "(({a} * (x ^ 2)) + ({b} * x * y) + ({c} * (y ^ 2)))", "scripts": {}, "customMarkingAlgorithm": "", "type": "jme", "answerSimplification": "std", "failureRate": 1, "variableReplacements": [], "vsetRangePoints": 5, "vsetRange": [0, 1], "checkingType": "absdiff", "variableReplacementStrategy": "originalfirst", "unitTests": [], "showCorrectAnswer": true, "marks": 2, "checkVariableNames": true, "showPreview": true, "extendBaseMarkingAlgorithm": true}, {"checkingAccuracy": 0.001, "showFeedbackIcon": true, "expectedVariableNames": ["x", "y"], "answer": "((({b} / 2) * (x ^ 2)) + ({(2 * c)} * x * y) + {d})", "scripts": {}, "customMarkingAlgorithm": "", "type": "jme", "answerSimplification": "std", "failureRate": 1, "variableReplacements": [], "vsetRangePoints": 5, "vsetRange": [0, 1], "checkingType": "absdiff", "variableReplacementStrategy": "originalfirst", "unitTests": [], "showCorrectAnswer": true, "marks": 2, "checkVariableNames": true, "showPreview": true, "extendBaseMarkingAlgorithm": true}], "customMarkingAlgorithm": "", "type": "gapfill", "variableReplacements": [], "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "unitTests": [], "prompt": "<p>Enter the partial derivatives here. Note if you want to enter a product of unknowns, such as $xy$ then you input the expression in the form <code>x*y</code>.</p>\n<p>$\\displaystyle { \\partial f \\over \\partial x}=$&nbsp;[[0]]</p>\n<p>$\\displaystyle {\\partial f \\over \\partial y}=$&nbsp;[[1]]</p>", "showCorrectAnswer": true, "marks": 0, "extendBaseMarkingAlgorithm": true}], "variables": {"other": {"description": "", "name": "other", "templateType": "anything", "definition": "if(s5=-1,'There can be no more stationary points as we cannot solve this.', if(ch=0,' we get the same stationary points',' You solve this getting 2 values of $x$ and then you obtain two more stationary points (which are not on the list you choose from).'))", "group": "Ungrouped variables"}, "check": {"description": "", "name": "check", "templateType": "anything", "definition": "if(ch=0, 'The two expressions for y in terms of x are the same and we will get exactly the same so ignore the rest!',' ')", "group": "Ungrouped variables"}, "s5": {"description": "", "name": "s5", "templateType": "anything", "definition": "if(d*(-b*d1+4*c*c1)<=0,-1,1)", "group": "Ungrouped variables"}, "m": {"description": "", "name": "m", "templateType": "anything", "definition": "random(1..4)", "group": "Ungrouped variables"}, "c": {"description": "", "name": "c", "templateType": "anything", "definition": "b1*d1", "group": "Ungrouped variables"}, "a1": {"description": "", "name": "a1", "templateType": "anything", "definition": "random(1..5)", "group": "Ungrouped variables"}, "d": {"description": "", "name": "d", "templateType": "anything", "definition": "-(b1*c1-3*a1*d1)/2*m^2", "group": "Ungrouped variables"}, "ch": {"description": "", "name": "ch", "templateType": "anything", "definition": "if(a1*d1=b1*c1,0,1)", "group": "Ungrouped variables"}, "c2": {"description": "", "name": "c2", "templateType": "anything", "definition": "random(1..4)", "group": "Ungrouped variables"}, "c1": {"description": "", "name": "c1", "templateType": "anything", "definition": "if(b1*c2=3*a1*d1,c2+1,c2)", "group": "Ungrouped variables"}, "a": {"description": "", "name": "a", "templateType": "anything", "definition": "a1*c1", "group": "Ungrouped variables"}, "d1": {"description": "", "name": "d1", "templateType": "anything", "definition": "random(2,4,6)", "group": "Ungrouped variables"}, "b1": {"description": "", "name": "b1", "templateType": "anything", "definition": "random(2,4,6)", "group": "Ungrouped variables"}, "b": {"description": "", "name": "b", "templateType": "anything", "definition": "b1*c1+a1*d1", "group": "Ungrouped variables"}}, "tags": [], "advice": "<h4>\\[\\begin{eqnarray*} {\\partial f \\over \\partial x} &amp;=&amp;\\simplify[std]{(({a} * (x ^ 2)) + ({b} * x * y) + ({c} * (y ^ 2)))}\\\\ \\\\ \\partial f \\over \\partial y &amp;=&amp;\\simplify[std]{((({b} / 2) * (x ^ 2)) + ({(2 * c)} * x * y) + {d})} \\end{eqnarray*}\\]</h4>\n<h4></h4>", "extensions": [], "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "preamble": {"js": "", "css": ""}, "metadata": {"description": "<p>Find the stationary points of the function: $f(x,y)=a x ^ 3 + b x ^ 2 y + c y ^ 2 x + dy$ by choosing from a list of points.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "\n  <p>Answer the following questions about the function:</p>\n  <p>\\[f(x,y)=\\simplify[std]{ ({a} / 3) * x ^ 3 + ({b} / 2) * x ^ 2 * y + {c} * y ^ 2 * x + {d} * y}\\]</p>\n  ", "type": "question", "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}