// Numbas version: finer_feedback_settings
{"name": "Maksimum og minimum f(x,y,z)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Maksimum og minimum f(x,y,z)", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>La funksjonen $f:X\\subseteq\\mathbb{R}^3\\rightarrow\\mathbb{R}$ v&aelig;re deriverbar i $\\mathbf{a}$.</p>", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>La $f_x(\\mathbf{a})=f_y(\\mathbf{a})=f_z(\\mathbf{a})=0$.</p>\n<p>La $d_1=f_{xx}(\\mathbf{a})$,&nbsp;$d_2=\\left| \\begin{array}{ccc} f_{xx}(\\mathbf{a}) &amp; f_{xy}(\\mathbf{a})&nbsp; \\\\ f_{yx}(\\mathbf{a}) &amp; f_{yy}(\\mathbf{a}) \\end{array}&nbsp;\\right|$,&nbsp; &nbsp;$d_3=\\left| \\begin{array}{ccc}&nbsp; f_{xx}(\\mathbf{a}) &amp; f_{xy}(\\mathbf{a}) &amp;&nbsp;f_{xx}(\\mathbf{a}) \\\\&nbsp;f_{yx}(\\mathbf{a}) &amp; f_{yy}(\\mathbf{a}) &amp;&nbsp;f_{yz}(\\mathbf{a}) \\\\&nbsp;f_{zx}(\\mathbf{a}) &amp;&nbsp;f_{zy}(\\mathbf{a}) &amp; f_{zz}(\\mathbf{a})\\end{array}&nbsp;\\right|$,&nbsp;&nbsp;</p>\n<p>Velg matchende p&aring;stander</p>", "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": false, "shuffleAnswers": true, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["$\\ $<br/>$d_1&lt;0 \\wedge d_2&gt;0 \\wedge d_3&lt;0$<br/>$\\ $", "$\\ $<br/>$d_1&gt;0 \\wedge d_2&gt;0 \\wedge d_3&gt;0$<br/>$\\ $", "$\\ $<br/>$d_3\\neq0$, men ingen av de to f&oslash;rste p&aring;standene er sanne<br/>$\\ $", "$\\ $<br/>$d_3=0$<br/>$\\ $"], "matrix": [["1", "0", 0, 0], ["0", "1", 0, 0], [0, 0, "1", 0], [0, 0, 0, "1"]], "layout": {"type": "all", "expression": ""}, "answers": ["$\\mathbf{a}$ er et lokalt maksimum", "$\\mathbf{a}$ er et lokalt&nbsp;minimum", "$\\mathbf{a}$ er et&nbsp;sadel punkt", "det kan ingenting sies om&nbsp;$\\mathbf{a}$"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Ida Friestad Pedersen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/792/"}, {"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}]}]}], "contributors": [{"name": "Ida Friestad Pedersen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/792/"}, {"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}]}