// Numbas version: finer_feedback_settings
{"name": "CF Maths Differentiation 15 - Applications Finding Gradient", "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", "b", "d", "g", "ee", "ans1", "tol"], "name": "CF Maths Differentiation 15 - Applications Finding Gradient", "tags": ["differentiation", "Differentiation", "fractional powers", "gradient at a point", "negative powers", "powers"], "type": "question", "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>", "rulesets": {"std": ["all", "fractionNumbers"]}, "parts": [{"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>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "showPrecisionHint": false, "maxValue": "ans1", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "minValue": "ans1", "type": "numberentry"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "{b}{a}x^({b}-1)-{d}{c}/x^({d}+1)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "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": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(2..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random(-3..3#0.01 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "ee": {"definition": "random(-10..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "ee", "description": ""}, "ans1": {"definition": "precround(a*b*g^(b-1)-c*d*g^(-d-1),2)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "tol": {"definition": "0.01", "templateType": "anything", "group": "Ungrouped variables", "name": "tol", "description": ""}}, "metadata": {"notes": "", "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"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/353/"}]}]}], "contributors": [{"name": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/353/"}]}