// Numbas version: finer_feedback_settings
{"name": "Differentiation 15 - Applications", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"js": "", "css": ""}, "ungrouped_variables": ["a", "c", "b", "d", "g", "ee", "ans1", "tol"], "advice": "<p>We have \\[\\frac{df}{dx}=\\var{a*b}x^{\\var{b-1}}-\\var{c*d}x^{\\var{-d-1}}\\]</p>\n<p>The gradient at $x=\\var{g}$ is given by the value of $\\displaystyle \\frac{df}{dx}$ at $x=\\var{g}$ and we therefore have:</p>\n<p>Gradient = $\\var{a*b}\\times(\\var{g})^{\\var{b-1}}-\\var{c*d}\\times (\\var{g})^{\\var{-d-1}}= \\var{dpformat(ans1,2)}$ to 2 decimal places.&nbsp;</p>", "metadata": {"description": "<p>Find the gradient of &nbsp;$ \\displaystyle ax^b+\\frac{c}{x^{d}}+f$ at $x=n$</p>", "licence": "Creative Commons Attribution 4.0 International"}, "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"customName": "", "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true, "useCustomName": false, "variableReplacements": [], "prompt": "<p>\\[ f(x) = \\simplify{ {a}*x^{b} + {c}/(x^{d}) + {ee}} \\]</p>\n<p>Firstly, differentiate.</p>\n<p>$f'(x)=$&nbsp;[[1]]</p>\n<p>Gradient at $x=\\var{g}\\;$ is&nbsp;[[0]]</p>", "unitTests": [], "gaps": [{"variableReplacementStrategy": "originalfirst", "precisionMessage": "You have not given your answer to the correct precision.", "customMarkingAlgorithm": "", "type": "numberentry", "showFeedbackIcon": true, "showPrecisionHint": false, "useCustomName": false, "minValue": "ans1", "marks": 1, "showCorrectAnswer": true, "precisionType": "dp", "mustBeReducedPC": 0, "maxValue": "ans1", "customName": "", "correctAnswerFraction": false, "precision": "2", "notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0, "scripts": {}, "strictPrecision": false, "allowFractions": false, "variableReplacements": [], "unitTests": [], "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "mustBeReduced": false}, {"variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "customMarkingAlgorithm": "", "type": "jme", "showFeedbackIcon": true, "useCustomName": false, "checkingAccuracy": 0.001, "vsetRangePoints": 5, "showCorrectAnswer": true, "marks": 1, "checkVariableNames": false, "valuegenerators": [{"value": "", "name": "x"}], "customName": "", "answer": "{b}{a}x^({b}-1)-{d}{c}/x^({d}+1)", "showPreview": true, "scripts": {}, "variableReplacements": [], "unitTests": [], "vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "failureRate": 1, "answerSimplification": "all"}], "showCorrectAnswer": true, "marks": 0, "extendBaseMarkingAlgorithm": true}], "tags": [], "statement": "<p><strong>Find the gradient of the curve $y= f(x)$ at the point, giving your answer to 2 decimal places.</strong></p>", "variables": {"c": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(2..7)", "name": "c"}, "ee": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(-10..10)", "name": "ee"}, "ans1": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "precround(a*b*g^(b-1)-c*d*g^(-d-1),2)", "name": "ans1"}, "d": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(2..5)", "name": "d"}, "b": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(2..5)", "name": "b"}, "a": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(2..5)", "name": "a"}, "g": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(-3..3#0.01 except 0)", "name": "g"}, "tol": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "0.01", "name": "tol"}}, "rulesets": {"std": ["all", "fractionNumbers"]}, "functions": {}, "extensions": [], "name": "Differentiation 15 - Applications", "type": "question", "contributors": [{"name": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}