// Numbas version: exam_results_page_options
{"name": "CATORCE CINCO Derivadas aplicaciones", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["z", "c", "b", "d", "f", "w", "a", "g", "h", "t", "maximum"], "name": "CATORCE CINCO Derivadas aplicaciones", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {"std": ["all", "fractionNumbers"]}, "parts": [{"prompt": "<p>Calcular la pendiente de la funci&oacute;n $y$ en el punto&nbsp;$x=\\var{d}$.</p>\n<p>\\[ y = \\simplify{ {a}*x^2 + {b}x + {c}} \\]</p>\n<p>En primer lugar, caculamos la primer derivada.</p>\n<p>$\\displaystyle \\frac{dy}{dx}=$&nbsp;[[1]]</p>\n<p><code>Ejemplo de respuesta: Escriba 3x+2, si la respuesta es </code>$3x+2$.</p>\n<p>La pendiente en el punto donde&nbsp;$x=\\var{d}\\;$ es:$f'(\\var{d})$=[[0]]</p>\n<p>Escriba el valor aproximado a dos cifras decimales.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "<p>Ingrese la respuesta con dos cifras decimales.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "2*a*d+b", "strictPrecision": false, "minValue": "2*a*d+b", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": "15", "showPrecisionHint": false, "type": "numberentry"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "2*{a}*x+{b}", "marks": "5", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Encuentre las coordenadas del punto en el cual la funci&oacute;n tiene un m&aacute;ximo o un m&iacute;nimo</p>\n<p>$y=\\simplify {{f}x^2+{g}x+{h}}$</p>\n<p>Determine la primer y segunda derivada $y$.</p>\n<p>$\\displaystyle \\frac{dy}{dx}=$&nbsp;[[2]]</p>\n<p>$\\displaystyle \\frac{d^2y}{dx^2}=$&nbsp;[[3]]</p>\n<p></p>\n<p>Calcular el valor cr&iacute;tico $x$ y $y$, tal que&nbsp;$\\displaystyle \\frac{dy}{dx}=0$.</p>\n<p>$x$-coordenada $=$&nbsp;[[0]]</p>\n<p>$y$-coordenada $=$&nbsp;[[1]]</p>\n<p>El punto es un m&aacute;ximo o un m&iacute;nimo&nbsp;[[4]]</p>\n<p></p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "<p>Ingrese la respuesta con dos cifras decimales.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "-g/(2*f)", "strictPrecision": false, "minValue": "-g/(2*f)", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": true, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": "15", "showPrecisionHint": false, "type": "numberentry"}, {"precisionType": "dp", "precisionMessage": "<p>Ingrese la respuesta con dos cifras decimales.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "g^2/(4*f)-g^2/(2*f)+h", "strictPrecision": false, "minValue": "g^2/(4*f)-g^2/(2*f)+h", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": true, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": "15", "showPrecisionHint": false, "type": "numberentry"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "2*{f}*x+{g}", "marks": "15", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "2*{f}", "marks": "5", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"displayColumns": 0, "matrix": ["if(maximum, 5, 0)", "if(maximum, 0, 5)"], "shuffleChoices": false, "variableReplacements": [], "choices": ["<p>maximum</p>", "<p>minimum</p>"], "variableReplacementStrategy": "originalfirst", "maxMarks": "0", "distractors": ["", ""], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "1_n_2", "displayType": "radiogroup", "minMarks": 0}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Una bola es lanzada verticalmente hacia arriba</p>\n<p>La posici&oacute;n est&aacute; dada por la f&oacute;rmula, con $t$ en segundos y $y$ en metros.</p>\n<p>\\[ y=\\var{z}t-\\var{w}t^2. \\]</p>\n<p>Cu&aacute;l es la m&aacute;xima altura alcanzada?</p>\n<p>Calculamos la primer derivada</p>\n<p>$\\displaystyle \\frac{dy}{dt}=$&nbsp;[[0]]</p>\n<p>El valor de la altura m&aacute;xima, aproximado a dos cifras decimales, es:</p>\n<p>$y=$&nbsp;[[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{z}-2*{w}*t", "marks": "20", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"precisionType": "dp", "precisionMessage": "<p>Ingrese la respuesta con dos cifras decimales.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "z^2/(4w)", "strictPrecision": false, "minValue": "z^2/(4w)", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": "5", "showPrecisionHint": false, "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(0..10#0.5)", "templateType": "randrange", "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(-10..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(-10..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "random(0..5#0.5)", "templateType": "randrange", "group": "Ungrouped variables", "name": "h", "description": ""}, "maximum": {"definition": "f<0", "templateType": "anything", "group": "Ungrouped variables", "name": "maximum", "description": "<p>Is the stationary point a maximum?</p>"}, "t": {"definition": "random(0..1#0.1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "t", "description": ""}, "w": {"definition": "random(2..5#0.1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "w", "description": ""}, "z": {"definition": "random(20..30#0.5)", "templateType": "randrange", "group": "Ungrouped variables", "name": "z", "description": ""}}, "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "contributors": [{"name": "Marlon Arcila", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/321/"}]}]}], "contributors": [{"name": "Marlon Arcila", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/321/"}]}