{"id":20120,"date":"2024-04-15T05:48:39","date_gmt":"2024-04-15T05:48:39","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=20120"},"modified":"2024-04-15T05:48:39","modified_gmt":"2024-04-15T05:48:39","slug":"the-function-fx-2x-x2-3-has-a-a-maxima-at-x-1-and-a-minima-at-x-5-b-a-maxima-at-x-1-and-a-minima-at-x-5-c-only-a-maxima-at-x-1-d-only-a-minima-at-x-1","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-function-fx-2x-x2-3-has-a-a-maxima-at-x-1-and-a-minima-at-x-5-b-a-maxima-at-x-1-and-a-minima-at-x-5-c-only-a-maxima-at-x-1-d-only-a-minima-at-x-1\/","title":{"rendered":"The function f(x) = 2x &#8211; x2 + 3 has A. a maxima at x = 1 and a minima at x = 5 B. a maxima at x = 1 and a minima at x = -5 C. only a maxima at x = 1 D. only a minima at x = 1"},"content":{"rendered":"<p>\r\n    <!-- Check if it's an AMP page -->\r\n            <!-- Non-AMP version -->\r\n        <div class=\"mcq-container\" data-quiz-id=\"quizState_6a97f1536b13f\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    a maxima at x = 1 and a minima at x = 5                <\/div>\r\n                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"true\">\r\n                    only a maxima at x = 1                <\/div>\r\n                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            \r\n            <!-- Feedback messages for non-AMP -->\r\n            <div class=\"feedback\" data-feedback=\"wrong\">Answer is Right!<\/div>\r\n            <div class=\"feedback\" data-feedback=\"right\">Answer is Wrong!<\/div>\r\n        <\/div>\r\n\r\n        <script>\r\n        document.addEventListener('DOMContentLoaded', function () {\r\n            var containers = document.querySelectorAll('.mcq-container');\r\n\r\n            containers.forEach(function(container) {\r\n                var options = container.querySelectorAll('.option');\r\n                var feedbackSelect = container.querySelector('[data-feedback=\"select\"]');\r\n                var feedbackWrong = container.querySelector('[data-feedback=\"wrong\"]');\r\n                var feedbackRight = container.querySelector('[data-feedback=\"right\"]');\r\n\r\n                options.forEach(function(option) {\r\n                    option.addEventListener('click', function() {\r\n                        var selectedOption = option.getAttribute('data-option-key');\r\n                        var isCorrect = option.getAttribute('data-is-correct') === 'true';\r\n\r\n                        \/\/ Remove previous selections\r\n                        options.forEach(function(opt) {\r\n                            opt.classList.remove('correct', 'incorrect');\r\n                        });\r\n\r\n                        \/\/ Add the correct\/incorrect class\r\n                        if (isCorrect) {\r\n                            option.classList.add('correct');\r\n                            feedbackRight.hidden = false;\r\n                            feedbackWrong.hidden = true;\r\n                        } else {\r\n                            option.classList.add('incorrect');\r\n                            feedbackRight.hidden = true;\r\n                            feedbackWrong.hidden = false;\r\n                        }\r\n\r\n                        \/\/ Hide select feedback\r\n                        feedbackSelect.hidden = true;\r\n                    });\r\n                });\r\n            });\r\n        });\r\n        <\/script>\r\n    \r\n    <!--more--><\/p>\n<p>The correct answer is: C. only a maxima at x = 1<\/p>\n<p>The function $f(x) = 2x &#8211; x^2 + 3$ is a parabola. The parabola opens upwards, so it has a maximum point. The maximum point occurs when $x = 1$.<\/p>\n<p>To find the maximum point, we can take the derivative of $f(x)$ and set it equal to zero. The derivative of $f(x)$ is $f'(x) = 2 &#8211; 2x$. Setting $f'(x) = 0$, we get $2 &#8211; 2x = 0$. Solving for $x$, we get $x = 1$.<\/p>\n<p>To verify that $x = 1$ is a maximum point, we can evaluate $f'(x)$ at $x = 1$. We get $f'(1) = 2 &#8211; 2(1) = 0$. Since $f'(1) = 0$, we know that $x = 1$ is a critical point. The derivative of a function is always zero at a critical point. If the derivative is positive on one side of the critical point and negative on the other side, then the critical point is a maximum point. In this case, the derivative of $f(x)$ is positive to the left of $x = 1$ and negative to the right of $x = 1$. Therefore, $x = 1$ is a maximum point.<\/p>\n<p>The other options are incorrect because they state that the function has a minimum point at $x = 1$. However, the function does not have a minimum point at $x = 1$. The function has a maximum point at $x = 1$.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Join Our Telegram Channel Subscribe on YouTube<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[690],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The function f(x) = 2x - x2 + 3 has A. a maxima at x = 1 and a minima at x = 5 B. a maxima at x = 1 and a minima at x = -5 C. only a maxima at x = 1 D. only a minima at x = 1<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/the-function-fx-2x-x2-3-has-a-a-maxima-at-x-1-and-a-minima-at-x-5-b-a-maxima-at-x-1-and-a-minima-at-x-5-c-only-a-maxima-at-x-1-d-only-a-minima-at-x-1\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The function f(x) = 2x - 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