// Numbas version: finer_feedback_settings
{"name": "Maria's copy of Differentiation: second derivatives, core facts", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"advice": "<p>See the resources listed at the top. If you're unsure of anything, then you are welcome to ask me.</p>", "tags": [], "functions": {}, "extensions": [], "name": "Maria's copy of Differentiation: second derivatives, core facts", "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "parts": [{"type": "m_n_x", "answers": ["<p>True</p>", "<p>False</p>"], "extendBaseMarkingAlgorithm": true, "maxAnswers": 0, "displayType": "radiogroup", "showFeedbackIcon": true, "matrix": "{marks}", "customName": "", "maxMarks": "0", "minMarks": 0, "prompt": "<p>Which of the following are true and which are false?</p>\n<p></p>\n<p>In the following,&nbsp;$f(x) = \\sin(x)$ and $g(t) = \\cos(t)$.</p>", "showCellAnswerState": true, "variableReplacements": [], "customMarkingAlgorithm": "", "layout": {"type": "all", "expression": ""}, "scripts": {}, "shuffleAnswers": false, "unitTests": [], "choices": "{statements}", "shuffleChoices": true, "showCorrectAnswer": true, "warningType": "none", "variableReplacementStrategy": "originalfirst", "marks": 0, "minAnswers": "{n}", "useCustomName": false}, {"type": "gapfill", "prompt": "<p>$f(x) = \\simplify{{a1}*x^{n1} + {b1}sin(x)}$.&nbsp; What is $\\frac{d^2 f}{dx^2}$?</p>\n<p>[[0]]</p>\n<p></p>\n<p></p>\n<p></p>\n<p>$g(t) = \\simplify{{a2}ln(t) + {b2} cos(t)}$. 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"variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "scripts": {}, "answer": "{-a2}/t^2 - {b2} cos(t)", "checkingType": "absdiff", "unitTests": [], "showCorrectAnswer": true, "vsetRangePoints": 5, "marks": "2", "useCustomName": false}], "extendBaseMarkingAlgorithm": true, "scripts": {}, "customName": "", "variableReplacementStrategy": "originalfirst", "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "sortAnswers": false, "variableReplacements": [], "marks": 0, "useCustomName": false}], "variables": {"b": {"templateType": "anything", "group": "change these", "name": "b", "definition": "random(10..18)+random(1..9)/10", "description": ""}, "statements_false": {"templateType": "anything", "group": "change these", "name": "statements_false", "definition": "[ \"$f''(x) = \\\\sin(x)$\",\n  \"$g''(t) = -\\\\cos(x)$\",\n  \"The first derivative of a function is different from the derivative of the function\",\n  \"The second derivative of $f$ is the derivative of $f$ \",\n  \"The second derivative of $g$ is denoted by $\\\\frac{d^2g}{d^2t} $\",\n  \"The second derivative of $g$ can be denoted by $\\\\frac{d^2g}{dx^2}$\",\n  \"If the second derivative of $f$ is positive, then the gradient of $f$ is positive\",\n  \"If the second derivative is positive, then the graph is concave\",\n  \"If the second derivative is negative, then the graph is convex\"\n  ]", "description": ""}, "c": {"templateType": "anything", "group": "change these", "name": "c", "definition": "random(6..9)", "description": ""}, "a1": {"templateType": "anything", "group": "part b", "name": "a1", "definition": "random(2..5)", "description": ""}, "rand": {"templateType": "anything", "group": "do not change these", "name": "rand", "definition": "repeat(random(0..1),n)", "description": ""}, "n1": {"templateType": "anything", "group": "part b", "name": "n1", "definition": "random(2..3)", "description": ""}, "b1": {"templateType": "anything", "group": "part b", 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$\\\\frac{d^2f}{dx^2}$\",\n  \"If the second derivative is positive, then the first derivative is increasing\",\n  \"If the second derivative is positive, then the graph is convex\",\n  \"If the second derivative is negative, then the graph is concave\"]\n ", "description": ""}, "max_mark": {"templateType": "anything", "group": "change these", "name": "max_mark", "definition": "5", "description": ""}, "marks": {"templateType": "anything", "group": "do not change these", "name": "marks", "definition": "matrix(map(if(rand[j]=1,[max_mark/n,-max_mark/3+max_mark/n],[-max_mark/3+max_mark/n,max_mark/n]),j,0..n-1))\n", "description": ""}, "b2": {"templateType": "anything", "group": "part b", "name": "b2", "definition": "random(-5..5 except [-1,0,1])", "description": ""}, "n": {"templateType": "anything", "group": "change these", "name": "n", "definition": "length(statements_true)", "description": ""}}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Q1 is true/false question covering some core facts, notation and basic examples.&nbsp; Q2 has two functions for which second derivative needs to be determined.</p>"}, "statement": "<p>This question deals with material found in&nbsp;these resources.</p>\n<ul>\n<li>From 0:40 to 1:50 of this <a href=\"https://www.youtube.com/watch?v=BLkz5LGWihw&amp;feature=youtu.be&amp;t=40\">YouTube video</a>.&nbsp; <strong>(The stuff&nbsp;beyond 1:50&nbsp;will be very confusing).</strong><strong></strong></li>\n</ul>", "variable_groups": [{"name": "change these", "variables": ["statements_true", "statements_false", "max_mark", "n", "a", "b", "c"]}, {"name": "do not change these", "variables": ["rand", "statements", "marks"]}, {"name": "part b", "variables": ["a1", "n1", "b1", "a2", "b2"]}], "preamble": {"css": "", "js": ""}, "rulesets": {}, "type": "question", "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}, {"name": "Maria 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