// Numbas version: finer_feedback_settings
{"name": "Maria's copy of Differentiation 15 - Applications", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"question_groups": [{"questions": [], "name": "", "pickQuestions": 0, "pickingStrategy": "all-ordered"}], "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>", "type": "question", "tags": ["differentiation", "Differentiation", "fractional powers", "gradient at a point", "negative powers", "powers"], "showQuestionGroupNames": false, "name": "Maria's copy of Differentiation 15 - Applications", "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "c", "b", "d", "g", "ee", "ans1", "tol"], "parts": [{"variableReplacements": [], "showCorrectAnswer": true, "gaps": [{"precisionType": "dp", "correctAnswerFraction": false, "type": "numberentry", "precision": "2", "minValue": "ans1", "allowFractions": false, "maxValue": "ans1", "strictPrecision": false, "scripts": {}, "precisionPartialCredit": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1, "precisionMessage": "You have not given your answer to the correct precision.", "showPrecisionHint": false}, {"type": "jme", "expectedvariablenames": [], "vsetrangepoints": 5, "variableReplacements": [], "vsetrange": [0, 1], "scripts": {}, "answer": "{b}{a}x^({b}-1)-{d}{c}/x^({d}+1)", "showpreview": true, "answersimplification": "all", "showCorrectAnswer": true, "checkingaccuracy": 0.001, "checkingtype": "absdiff", "checkvariablenames": false, "variableReplacementStrategy": "originalfirst", "marks": 1}], "scripts": {}, "variableReplacementStrategy": "originalfirst", "marks": 0, "type": "gapfill", "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>"}], "variables": {"b": {"templateType": "anything", "definition": "random(2..5)", "name": "b", "group": "Ungrouped variables", "description": ""}, "c": {"templateType": "anything", "definition": "random(2..7)", "name": "c", "group": "Ungrouped variables", "description": ""}, "ee": {"templateType": "anything", "definition": "random(-10..10)", "name": "ee", "group": "Ungrouped variables", "description": ""}, "g": {"templateType": "anything", "definition": "random(-3..3#0.01 except 0)", "name": "g", "group": "Ungrouped variables", "description": ""}, "d": {"templateType": "anything", "definition": "random(2..5)", "name": "d", "group": "Ungrouped variables", "description": ""}, "a": {"templateType": "anything", "definition": "random(2..5)", "name": "a", "group": "Ungrouped variables", "description": ""}, "ans1": {"templateType": "anything", "definition": "precround(a*b*g^(b-1)-c*d*g^(-d-1),2)", "name": "ans1", "group": "Ungrouped variables", "description": ""}, "tol": {"templateType": "anything", "definition": "0.01", "name": "tol", "group": "Ungrouped variables", "description": ""}}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Find the gradient of &nbsp;$ \\displaystyle ax^b+\\frac{c}{x^{d}}+f$ at $x=n$</p>", "notes": ""}, "statement": "<p><strong>Find the gradient of the curve $y= f(x)$ at the point, giving your answer to 2 decimal places.</strong></p>", "variable_groups": [], "preamble": {"css": "", "js": ""}, "functions": {}, "rulesets": {"std": ["all", "fractionNumbers"]}, "contributors": [{"name": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}]}], "contributors": [{"name": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}