{"id":4291,"date":"2018-04-16T03:46:44","date_gmt":"2018-04-16T03:46:44","guid":{"rendered":"https:\/\/www.helpingstudents.com.ng\/?p=4291"},"modified":"2020-03-03T05:35:17","modified_gmt":"2020-03-03T05:35:17","slug":"22-questions-on-differentiation","status":"publish","type":"post","link":"https:\/\/hstutorial.com\/fr\/22-questions-on-differentiation\/","title":{"rendered":"22 Questions on Differentiation"},"content":{"rendered":"<h4>Differentiation from First Principles<\/h4>\n<ol>\n<li>Differentiate the function; y = x<\/li>\n<li>Differentiate the function; y = x<sup>2<\/sup><\/li>\n<li>Find the derivative of\u00a0 \u00a0 \u00a0 \u00a0 \u00a0y =\u00a0 1\/x<\/li>\n<li>Find the derivative of\u00a0 \u00a0 \u00a0 \u00a0 \u00a0y = sinx<\/li>\n<\/ol>\n<h4>Differentiation from General Formula<\/h4>\n<ol start=\"5\">\n<li>Differentiate y = 5x<sup>3<\/sup> \u2013 7x<sup>2 <\/sup>+ 100x + 9<\/li>\n<li>Find the gradient of the function: y = 3x<sup>2<\/sup> + 5x \u2013 7 at x = 1<\/li>\n<\/ol>\n<h4>Product Rule of Differentiation<\/h4>\n<ol start=\"7\">\n<li>If y = (2x + 5)(6x<sup>2<\/sup> + 7x \u2013 1),\u00a0 \u00a0\u00a0\u00a0find dy\/dx<\/li>\n<li>If y = x \u00a0,\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 find\u00a0dy\/dx<\/li>\n<\/ol>\n<h4>Composite Rule of Differentiation<\/h4>\n<ol start=\"9\">\n<li>If y = (3x + 5)<sup>7<\/sup> ,\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 find\u00a0dy\/dx<\/li>\n<li>If y = \u00a0,\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 find\u00a0dy\/dx<\/li>\n<\/ol>\n<h4>Quotient Rule of Differentiation<\/h4>\n<ol start=\"11\">\n<li>If y = \u00a0,\u00a0\u00a0\u00a0\u00a0 find\u00a0dy\/dx<\/li>\n<\/ol>\n<h4>Maximum and Minimum Points<\/h4>\n<ol start=\"12\">\n<li>For the function y = x<sup>2 <\/sup>\u2013 5x<\/li>\n<\/ol>\n<p>Find:<\/p>\n<ul>\n<li>The turning point.<\/li>\n<li>The maximum or minimum point.<\/li>\n<li>The maximum or minimum value.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ol start=\"13\">\n<li>Distinguish between the maximum and minimum points of the function 12x \u2013 x<sup>3<\/sup>. Find also the maximum and minimum values.<\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<ol start=\"14\">\n<li>For the function<\/li>\n<\/ol>\n<p>Y = x<sup>3<\/sup> \u2013 5x<sup>2<\/sup> + 7x + 2<\/p>\n<p>Determine the turning points and distinguish between them. Find also the maximum and minimum values.<\/p>\n<h4>Application of Differentiation in Business Studies<\/h4>\n<ol start=\"15\">\n<li>The price (p) of a product is given by:<\/li>\n<\/ol>\n<p>P = 175 \u2013 4q<\/p>\n<p>And the total cost of the product is<\/p>\n<p>C = 1980 + 2q + 0.02q<sup>2<\/sup><\/p>\n<p>Determine:<\/p>\n<ul>\n<li>The revenue function.<\/li>\n<li>The revenue when quantity is 6.<\/li>\n<li>The marginal revenue.<\/li>\n<li>When the marginal revenue equals zero.<\/li>\n<li>The marginal cost.<\/li>\n<li>When the marginal revenue equals marginal cost.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ol start=\"16\">\n<li>CharllyCARES Nigeria Ltd. Has expressed the monthly demand function of one of the company\u2019s products as:<\/li>\n<\/ol>\n<p>P = 3(12 \u2013 q)<\/p>\n<p>Where p = unit price (N) and q = quantity demanded while the cost of production C is expressed as:<\/p>\n<p>C = 15(12 \u2013 q).<\/p>\n<p>Find:<\/p>\n<ul>\n<li>The total monthly revenue of the company in terms of the quantity demanded.<\/li>\n<li>The monthly profit of the company.<\/li>\n<li>The break-even point(s) and explain the significance as related to the profit of Charlly\u2019s company.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ol start=\"17\">\n<li>The price (p) of a commodity in a company is given by<\/li>\n<\/ol>\n<p>P = 120 &#8211; \u00a0and the total cost of the commodity in a month of the year 2002 is C = 40x where X is the quantity demanded.<\/p>\n<p>Determine:<\/p>\n<ul>\n<li>The revenue function.<\/li>\n<li>The revenue when x = 50 units.<\/li>\n<li>The marginal revenue.<\/li>\n<li>The profit function.<\/li>\n<li>The profit when x = 105 units.<\/li>\n<li>When the profit is maximized.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ol start=\"18\">\n<li>Soft Study Nigeria Ltd started a library business in June 2000. If the stock of books, y, after x months of production is:<\/li>\n<\/ol>\n<p>Y = 2x<sup>3<\/sup> \u00a03 \u2013 15x<sup>2 <\/sup>+ 88x<\/p>\n<p>When would the company have the:<\/p>\n<ul>\n<li>The largest number of books and how many?<\/li>\n<li>Least number of books and how many?<\/li>\n<\/ul>\n<ol start=\"19\">\n<li>A company newly bought machine is said to be depreciating. So after x years, its value is expressed as:<\/li>\n<\/ol>\n<p>Y = 16500e<sup>&#8211; 0.2x<\/sup><\/p>\n<ul>\n<li>At what rate will the machine depreciate after 5 years?<\/li>\n<li>At what percentage rate will the value depreciate after the five years?<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ol start=\"20\">\n<li>The demand for the product of a company is given by:<\/li>\n<\/ol>\n<p>3p = 9q<sup>2<\/sup> \u2013 540<\/p>\n<p>While the supply function is given by:<\/p>\n<p>P = 30q \u2013 63<\/p>\n<p>Determine:<\/p>\n<ul>\n<li>The equilibrium price and quantity.<\/li>\n<li>The elasticity of supply when q = 5 units<\/li>\n<\/ul>\n<ol start=\"21\">\n<li>The demand for one of a company\u2019s product is exponentially distributed with:<\/li>\n<\/ol>\n<p>Y = 150e<sup>&#8211; 0.02p<\/sup><\/p>\n<p>Units per day at a market price of p Naira. What price will there be the greatest customer\u2019s demand?<\/p>\n<p>&nbsp;<\/p>\n<ol start=\"22\">\n<li>The price of Ada\u2019s juice per unit is given by:<\/li>\n<\/ol>\n<p>P = 50q \u2013 q<sup>2<\/sup> \u2013 800<\/p>\n<p>While the total cost of producing the juice is:<\/p>\n<p>C = 800 + 700q \u2013 3q<sup>2<\/sup> + q<sup>3<\/sup><\/p>\n<ul>\n<li>Determine the quantity which maximizes the profit.<\/li>\n<li>How many units of the juice needs to be produced in order to maximize profit if the selling price remains at N700.<\/li>\n<\/ul>","protected":false},"excerpt":{"rendered":"<p>Differentiation from First Principles Differentiate the function; y = x Differentiate the function; y = x2 Find the derivative of\u00a0 \u00a0 \u00a0 \u00a0 \u00a0y =\u00a0 1\/x Find the derivative of\u00a0 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/hstutorial.com\/fr\/22-questions-on-differentiation\/\"> <span class=\"screen-reader-text\">22 Questions on Differentiation<\/span> Lire la suite \"<\/a><\/p>","protected":false},"author":2,"featured_media":4518,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"footnotes":""},"categories":[55],"tags":[229,170],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.5 (Yoast SEO v21.5) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>22 Questions on Differentiation - HS Tutorial<\/title>\n<meta name=\"description\" content=\"Differentiation. 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