{"id":48,"date":"2015-09-22T15:30:00","date_gmt":"2015-09-22T15:30:00","guid":{"rendered":"https:\/\/sites.udmercy.edu\/archeyde\/?p=48"},"modified":"2025-02-21T18:41:35","modified_gmt":"2025-02-21T23:41:35","slug":"derivatives-and-rate-of-change","status":"publish","type":"post","link":"https:\/\/sites.udmercy.edu\/archeyde\/2015\/09\/22\/derivatives-and-rate-of-change\/","title":{"rendered":"Derivatives and Rate of Change"},"content":{"rendered":"

Here are two problems I used in my calculus 1 class, just after teaching them the definition of the derivative and discussing average and instantaneous rates of change.<\/p>\n

 <\/p>\n

    \n
  1. My car has a digital read out with the average fuel economy.\u00a0 I used to have a car which also had the instantaneous fuel economy.
    \n\"AverageFuelEconomy\"<\/a>
    \nWhat is the difference between these two fuel economies?\u00a0 Under what circumstances is each more useful?\u00a0 How can I use the average fuel economy feature to approximate my instantaneous fuel economy?\u00a0 (Your answer should be\u00a0 2-5 complete sentences).<\/li>\n
  2. Read the article at
    \n     http:\/\/www.slate.com\/blogs\/bad_astronomy\/2015\/09\/03\/ice_loss_greenland_and_antarctica_lost_5_trillion_tons_since_1992.html<\/a> .
    \nYou can use this QR code to access it
    \n    \"QR-code-ice-melt\"<\/a><\/li>\n
  3. Then answer the following questions. Give all answers in complete sentences with units.<\/li>\n<\/ol>\n
      \n
    • What is the average rate of change of the mass of Antarctica’s ice?<\/li>\n
    • What is the average rate of change of the mass of Greenland’s ice?<\/li>\n
    • Looking at the graphs, do you think it is reasonable to talk about the instantaneous rate of change for these quantities?\u00a0 Why or why not?<\/li>\n<\/ul>\n

       <\/p>\n","protected":false},"excerpt":{"rendered":"

      Here are two problems I used in my calculus 1 class, just after teaching them the definition of the derivative and discussing average and instantaneous rates of change.   My car has a digital read out with the average fuel economy.\u00a0 I used to have a car which also had the instantaneous fuel economy. What […]<\/p>\n","protected":false},"author":154,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[12265],"tags":[12266,12251,12263,12259,12260,12262],"_links":{"self":[{"href":"https:\/\/sites.udmercy.edu\/archeyde\/wp-json\/wp\/v2\/posts\/48"}],"collection":[{"href":"https:\/\/sites.udmercy.edu\/archeyde\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.udmercy.edu\/archeyde\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.udmercy.edu\/archeyde\/wp-json\/wp\/v2\/users\/154"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.udmercy.edu\/archeyde\/wp-json\/wp\/v2\/comments?post=48"}],"version-history":[{"count":6,"href":"https:\/\/sites.udmercy.edu\/archeyde\/wp-json\/wp\/v2\/posts\/48\/revisions"}],"predecessor-version":[{"id":217,"href":"https:\/\/sites.udmercy.edu\/archeyde\/wp-json\/wp\/v2\/posts\/48\/revisions\/217"}],"wp:attachment":[{"href":"https:\/\/sites.udmercy.edu\/archeyde\/wp-json\/wp\/v2\/media?parent=48"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.udmercy.edu\/archeyde\/wp-json\/wp\/v2\/categories?post=48"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.udmercy.edu\/archeyde\/wp-json\/wp\/v2\/tags?post=48"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}