{"id":238970,"date":"2025-06-18T14:05:52","date_gmt":"2025-06-18T14:05:52","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=238970"},"modified":"2025-06-18T14:05:54","modified_gmt":"2025-06-18T14:05:54","slug":"estimate-fx-and-fy-at-point-b","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/18\/estimate-fx-and-fy-at-point-b\/","title":{"rendered":"Estimate\u00a0fx\u00a0and\u00a0fy\u00a0at point B"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/image-722.png\" alt=\"\" class=\"wp-image-238971\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The estimated partial derivatives at point B are:<\/p>\n\n\n\n<p>fx(B) \u2248 2.5<\/p>\n\n\n\n<p>fy(B) \u2248 -10<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>Partial derivatives represent the rate of change of a function with respect to one variable while holding the other variable constant. In this case, fx measures the rate of change of f with respect to x while fy measures the rate of change with respect to y.<\/p>\n\n\n\n<p>To estimate fx at point B, we analyze the contour lines in the region surrounding B. Point B is located between the contour lines labeled 0 and 10. Moving in the positive x-direction from B, the function value increases from 0 to 10 over a horizontal distance of approximately 4 units. The rate of change is found by dividing the change in function value by the change in x:<\/p>\n\n\n\n<p>fx(B) \u2248 (10 &#8211; 0) \/ (2 &#8211; (-2)) = 10 \/ 4 = 2.5<\/p>\n\n\n\n<p>Next, to estimate fy at point B, we examine the function\u2019s variation along the y-axis. Point B is situated between the contour lines labeled 0 and -10. Moving vertically upward, the function value decreases from 0 to -10 over a vertical distance of approximately 1 unit. The rate of change in the function due to a change in y is:<\/p>\n\n\n\n<p>fy(B) \u2248 (-10 &#8211; 0) \/ (1 &#8211; 0) = -10 \/ 1 = -10<\/p>\n\n\n\n<p>These derivatives indicate how the function changes near point B. A positive fx suggests an increase in function value as x increases, while a negative fy signifies a decrease as y increases. This information can be useful in understanding the local behavior of f(x, y) and how it varies across the coordinate plane.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1126.jpeg\" alt=\"\" class=\"wp-image-238972\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: The estimated partial derivatives at point B are: fx(B) \u2248 2.5 fy(B) \u2248 -10 Explanation Partial derivatives represent the rate of change of a function with respect to one variable while holding the other variable constant. In this case, fx measures the rate of change of f with respect [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-238970","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238970","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=238970"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238970\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=238970"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=238970"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=238970"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}