{"id":3354,"date":"2025-06-05T04:31:39","date_gmt":"2025-06-05T04:31:39","guid":{"rendered":"https:\/\/diznr.com\/?p=3354"},"modified":"2025-06-05T04:31:39","modified_gmt":"2025-06-05T04:31:39","slug":"cseit-gate-1997-subject-engineering-mathematic-topic-calulus-what-is-the-value-maximum","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/cseit-gate-1997-subject-engineering-mathematic-topic-calulus-what-is-the-value-maximum\/","title":{"rendered":"CSEIT &#8211; GATE 1997 Subject &#8211; Engineering Mathematic\/ Topic &#8211; Calulus What is the maximum value."},"content":{"rendered":"<p>CSEIT &#8211; GATE 1997 Subject &#8211; Engineering Mathematic\/ Topic &#8211; Calulus What is the maximum value.<\/p>\n<p>[fvplayer id=&#8221;367&#8243;]<\/p>\n<p data-start=\"0\" data-end=\"107\">In the GATE 1997 exam for Computer Science and Engineering (CSE), a calculus question was posed as follows:<\/p>\n<p data-start=\"109\" data-end=\"219\"><strong data-start=\"109\" data-end=\"122\">Question:<\/strong> What is the maximum value of the function <span class=\"katex\"><span class=\"katex-mathml\">f(x)=2&#215;2\u22122x+6f(x) = 2x^2 &#8211; 2x + 6<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">6<\/span><\/span><\/span><\/span> in the interval <span class=\"katex\"><span class=\"katex-mathml\">[0,2][0, 2]<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">[<\/span><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">2<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span>?<\/p>\n<p data-start=\"221\" data-end=\"234\"><strong data-start=\"221\" data-end=\"234\">Solution:<\/strong><\/p>\n<ol data-start=\"236\" data-end=\"1255\">\n<li data-start=\"236\" data-end=\"420\">\n<p data-start=\"239\" data-end=\"296\"><strong data-start=\"239\" data-end=\"296\">Evaluate <span class=\"katex\"><span class=\"katex-mathml\">f(x)f(x)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> at the endpoints of the interval:<\/strong><\/p>\n<ul data-start=\"301\" data-end=\"420\">\n<li data-start=\"301\" data-end=\"358\">\n<p data-start=\"303\" data-end=\"358\">At <span class=\"katex\"><span class=\"katex-mathml\">x=0x = 0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><\/span><\/span><\/span>: <span class=\"katex\"><span class=\"katex-mathml\">f(0)=2(0)2\u22122(0)+6=6f(0) = 2(0)^2 &#8211; 2(0) + 6 = 6<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">0<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">0<\/span><span class=\"mclose\">)<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">0<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">6<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">6<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li data-start=\"363\" data-end=\"420\">\n<p data-start=\"365\" data-end=\"420\">At <span class=\"katex\"><span class=\"katex-mathml\">x=2x = 2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><\/span><\/span><\/span>: <span class=\"katex\"><span class=\"katex-mathml\">f(2)=2(2)2\u22122(2)+6=8f(2) = 2(2)^2 &#8211; 2(2) + 6 = 8<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">2<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">2<\/span><span class=\"mclose\">)<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">2<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">6<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">8<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n<\/li>\n<li data-start=\"422\" data-end=\"726\">\n<p data-start=\"425\" data-end=\"520\"><strong data-start=\"425\" data-end=\"520\">Find the critical points within the interval by setting the derivative <span class=\"katex\"><span class=\"katex-mathml\">f\u2032(x)f'(x)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> to zero:<\/strong><\/p>\n<ul data-start=\"525\" data-end=\"726\">\n<li data-start=\"525\" data-end=\"613\">\n<p data-start=\"527\" data-end=\"613\">First, compute the derivative: <span class=\"katex\"><span class=\"katex-mathml\">f\u2032(x)=ddx(2&#215;2\u22122x+6)=4x\u22122f'(x) = \\frac{d}{dx}(2x^2 &#8211; 2x + 6) = 4x &#8211; 2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">6<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li data-start=\"618\" data-end=\"726\">\n<p data-start=\"620\" data-end=\"726\">Set the derivative equal to zero to find critical points: <span class=\"katex\"><span class=\"katex-mathml\">4x\u22122=04x &#8211; 2 = 0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">4<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><\/span><\/span><\/span> <span class=\"katex\"><span class=\"katex-mathml\">x=12x = \\frac{1}{2}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n<\/li>\n<li data-start=\"728\" data-end=\"961\">\n<p data-start=\"731\" data-end=\"799\"><strong data-start=\"731\" data-end=\"799\">Evaluate <span class=\"katex\"><span class=\"katex-mathml\">f(x)f(x)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> at the critical point <span class=\"katex\"><span class=\"katex-mathml\">x=12x = \\frac{1}{2}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>:<\/strong><\/p>\n<p data-start=\"804\" data-end=\"961\"><span class=\"katex\"><span class=\"katex-mathml\">f(12)=2(12)2\u22122(12)+6=2(14)\u22121+6=12\u22121+6=5.5f\\left(\\frac{1}{2}\\right) = 2\\left(\\frac{1}{2}\\right)^2 &#8211; 2\\left(\\frac{1}{2}\\right) + 6 = 2\\left(\\frac{1}{4}\\right) &#8211; 1 + 6 = \\frac{1}{2} &#8211; 1 + 6 = 5.5<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"minner\"><span class=\"mopen delimcenter\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"minner\"><span class=\"mopen delimcenter\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\"><span class=\"delimsizing size1\">)<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"minner\"><span class=\"mopen delimcenter\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">6<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"minner\"><span class=\"mopen delimcenter\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">4<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">6<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">6<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">5.5<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li data-start=\"963\" data-end=\"1255\">\n<p data-start=\"966\" data-end=\"998\"><strong data-start=\"966\" data-end=\"998\">Determine the maximum value:<\/strong><\/p>\n<p data-start=\"1003\" data-end=\"1073\">Comparing the function values at the endpoints and the critical point:<\/p>\n<ul data-start=\"1077\" data-end=\"1156\">\n<li data-start=\"1077\" data-end=\"1093\"><span class=\"katex\"><span class=\"katex-mathml\">f(0)=6f(0) = 6<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">0<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">6<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"1097\" data-end=\"1136\"><span class=\"katex\"><span class=\"katex-mathml\">f(12)=5.5f\\left(\\frac{1}{2}\\right) = 5.5<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"minner\"><span class=\"mopen delimcenter\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">5.5<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"1140\" data-end=\"1156\"><span class=\"katex\"><span class=\"katex-mathml\">f(2)=8f(2) = 8<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">2<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">8<\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<p data-start=\"1161\" data-end=\"1255\">The maximum value of <span class=\"katex\"><span class=\"katex-mathml\">f(x)f(x)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> on the interval <span class=\"katex\"><span class=\"katex-mathml\">[0,2][0, 2]<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">[<\/span><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">2<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span> is <strong data-start=\"1223\" data-end=\"1228\">8<\/strong>, occurring at <span class=\"katex\"><span class=\"katex-mathml\">x=2x = 2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><\/span><\/span><\/span>.<\/p>\n<\/li>\n<\/ol>\n<p data-start=\"1257\" data-end=\"1366\"><strong data-start=\"1257\" data-end=\"1268\">Answer:<\/strong> The maximum value of the function <span class=\"katex\"><span class=\"katex-mathml\">f(x)=2&#215;2\u22122x+6f(x) = 2x^2 &#8211; 2x + 6<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">6<\/span><\/span><\/span><\/span> in the interval <span class=\"katex\"><span class=\"katex-mathml\">[0,2][0, 2]<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">[<\/span><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">2<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span> is <strong data-start=\"1360\" data-end=\"1365\">8<\/strong>.<\/p>\n<p data-start=\"1368\" data-end=\"1572\">This solution aligns with the analysis provided on GATE Overflow, where the function&#8217;s behavior within the given interval was examined to determine the maximum value.<\/p>\n<h3 class=\"relative inline-flex items-center\"><a href=\"http:\/\/files.hostgator.co.in\/hostgator252048\/file\/gatemathematicsquestionsallbranchbyskmondal.pdf\" target=\"_blank\" rel=\"noopener\">CSEIT &#8211; GATE 1997 Subject &#8211; Engineering Mathematic\/ Topic &#8211; Calulus What is the maximum value.<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/www.vidyalankar.org\/gate\/assets\/docs\/notes\/maths.pdf\" target=\"_blank\" rel=\"noopener\">Engineering Mathematics Notes<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\">Calculus.pdf<\/h3>\n<p data-start=\"0\" data-end=\"178\">Your question refers to a GATE 1997 question from the CSE\/IT paper in the subject of <strong data-start=\"85\" data-end=\"112\">Engineering Mathematics<\/strong>, specifically the <strong data-start=\"131\" data-end=\"143\">Calculus<\/strong> topic. However, you&#8217;ve only asked:<\/p>\n<blockquote data-start=\"180\" data-end=\"210\">\n<p data-start=\"182\" data-end=\"210\">&#8220;What is the maximum value?&#8221;<\/p>\n<\/blockquote>\n<p data-start=\"212\" data-end=\"373\">To help you correctly, I need the full question or function you&#8217;re referring to. For example, in Calculus, typical questions about maximum value might look like:<\/p>\n<ul data-start=\"375\" data-end=\"583\">\n<li data-start=\"375\" data-end=\"444\">\n<p data-start=\"377\" data-end=\"444\">&#8220;What is the maximum value of the function <span class=\"katex\"><span class=\"katex-mathml\">f(x)=x(10\u2212x)f(x) = x(10 &#8211; x)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">10<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span>?&#8221;<\/p>\n<\/li>\n<li data-start=\"445\" data-end=\"509\">\n<p data-start=\"447\" data-end=\"509\">&#8220;Find the maximum value of <span class=\"katex\"><span class=\"katex-mathml\">sin\u2061x+cos\u2061x\\sin x + \\cos x<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mop\">sin<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mop\">cos<\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span> on [0, \u03c0\/2].&#8221;<\/p>\n<\/li>\n<li data-start=\"510\" data-end=\"583\">\n<p data-start=\"512\" data-end=\"583\">&#8220;What is the maximum value of a given polynomial or rational function?&#8221;<\/p>\n<\/li>\n<\/ul>\n<p data-start=\"585\" data-end=\"699\" data-is-last-node=\"\" data-is-only-node=\"\">Please provide the complete question, equation, or expression so I can help you find the maximum value accurately.<\/p>\n<h3 data-start=\"585\" data-end=\"699\"><a href=\"https:\/\/gnindia.dronacharya.info\/CSE\/Downloads\/Sub_info\/1stYear\/Gate\/Maths.pdf\" target=\"_blank\" rel=\"noopener\">CSEIT &#8211; GATE 1997 Subject &#8211; Engineering Mathematic\/ Topic &#8211; Calulus What is the maximum value.<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/www.govinfo.gov\/content\/pkg\/GOVPUB-C13-3fa03b5da58fa1f9872190856cdccef3\/pdf\/GOVPUB-C13-3fa03b5da58fa1f9872190856cdccef3.pdf\" target=\"_blank\" rel=\"noopener\">Mathematics and engineering in computer science<\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"<p>CSEIT &#8211; GATE 1997 Subject &#8211; Engineering Mathematic\/ Topic &#8211; Calulus What is the maximum value. [fvplayer id=&#8221;367&#8243;] In the GATE 1997 exam for Computer Science and Engineering (CSE), a calculus question was posed as follows: Question: What is the maximum value of the function f(x)=2&#215;2\u22122x+6f(x) = 2x^2 &#8211; 2x + 6f(x)=2&#215;2\u22122x+6 in the interval [&hellip;]<\/p>\n","protected":false},"author":66,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[103],"tags":[],"class_list":["post-3354","post","type-post","status-publish","format-standard","hentry","category-engineering-mathematics"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3354","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/users\/66"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/comments?post=3354"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3354\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=3354"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=3354"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=3354"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}