{"id":4278,"date":"2022-06-10T20:27:27","date_gmt":"2022-06-10T20:27:27","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=4278"},"modified":"2022-06-10T20:27:27","modified_gmt":"2022-06-10T20:27:27","slug":"interpretation-of-derivatives","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/06\/10\/interpretation-of-derivatives\/","title":{"rendered":"Interpretation of Derivatives"},"content":{"rendered":"\n<p>The derivative is a function that is geometrically defined as the slope of the line tangent to the curve at any point. If f is differentiable and continuous at [a,b], then<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code> f'(x) = lim <sub>h\u21920<\/sub> f(x+h)\u2212f(x)\/h\n lim <sub>h\u21920<\/sub> f(x+h)\u2212f(x)h.<\/code><\/pre>\n\n\n\n<p> This change in h is infinitely very small. We denote it by \u0394x. Then change in the original function f(x) is also small, denoted by \u0394y. The derivative so obtained by applying the limits is also defined as the instantaneous rate of change of a function with respect to a variable.&nbsp;<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">f'(x) =&nbsp;\u0394y\/\u0394x = lim <sub>x\u21920<\/sub> f(x+\u03b4x)\u2212f(x) \/\u03b4x\u0394 y\u0394x =lim\u03b4x\u21920f(x+\u03b4x)\u2212f(x)\u03b4x.<\/pre>\n\n\n\n<p>If the derivative &gt; 0, then the curve is increasing, and if the derivative &lt; 0, then the curve is decreasing. The derivative at any stationary point = 0 which implies that the function is neither increasing nor decreasing.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The derivative is a function that is geometrically defined as the slope of the line tangent to the curve at any point. If f is differentiable and continuous at [a,b], then This change in h is infinitely very small. We denote it by \u0394x. Then change in the original function f(x) is also small, denoted [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[799],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/4278"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=4278"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/4278\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=4278"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=4278"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=4278"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}