What does it mean for a function to be semi-monotonic?











up vote
0
down vote

favorite












I mostly understand monotonic functions as described by wikipedia. However, I do not understand what it means for a function to be semi-monotonic as described in the java math class. This page helped a little bit but I still don't understand it. The list below is the best that I can explain what I'm trying to figure out since I don't know what I don't know.




  1. Does monotonicity apply only to the signs' of the mathematical function's and its corresponding approximation's first derivative or does it make sense to say that the monotonicity of $sin(fracpi4)$ is $frac{sqrt2}{2}$ since the value of its first derivative at $fracpi4$ is $frac{sqrt2}{2}$?

  2. How can you prove that an approximation of a differentiable function is semi-monotonic?

  3. Can you think of an approximation of sine or any other differentiable function that closely represents the actual function, but the derivative of that approximation does not represent the derivative of the actual function's derivative?










share|cite|improve this question


























    up vote
    0
    down vote

    favorite












    I mostly understand monotonic functions as described by wikipedia. However, I do not understand what it means for a function to be semi-monotonic as described in the java math class. This page helped a little bit but I still don't understand it. The list below is the best that I can explain what I'm trying to figure out since I don't know what I don't know.




    1. Does monotonicity apply only to the signs' of the mathematical function's and its corresponding approximation's first derivative or does it make sense to say that the monotonicity of $sin(fracpi4)$ is $frac{sqrt2}{2}$ since the value of its first derivative at $fracpi4$ is $frac{sqrt2}{2}$?

    2. How can you prove that an approximation of a differentiable function is semi-monotonic?

    3. Can you think of an approximation of sine or any other differentiable function that closely represents the actual function, but the derivative of that approximation does not represent the derivative of the actual function's derivative?










    share|cite|improve this question
























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      I mostly understand monotonic functions as described by wikipedia. However, I do not understand what it means for a function to be semi-monotonic as described in the java math class. This page helped a little bit but I still don't understand it. The list below is the best that I can explain what I'm trying to figure out since I don't know what I don't know.




      1. Does monotonicity apply only to the signs' of the mathematical function's and its corresponding approximation's first derivative or does it make sense to say that the monotonicity of $sin(fracpi4)$ is $frac{sqrt2}{2}$ since the value of its first derivative at $fracpi4$ is $frac{sqrt2}{2}$?

      2. How can you prove that an approximation of a differentiable function is semi-monotonic?

      3. Can you think of an approximation of sine or any other differentiable function that closely represents the actual function, but the derivative of that approximation does not represent the derivative of the actual function's derivative?










      share|cite|improve this question













      I mostly understand monotonic functions as described by wikipedia. However, I do not understand what it means for a function to be semi-monotonic as described in the java math class. This page helped a little bit but I still don't understand it. The list below is the best that I can explain what I'm trying to figure out since I don't know what I don't know.




      1. Does monotonicity apply only to the signs' of the mathematical function's and its corresponding approximation's first derivative or does it make sense to say that the monotonicity of $sin(fracpi4)$ is $frac{sqrt2}{2}$ since the value of its first derivative at $fracpi4$ is $frac{sqrt2}{2}$?

      2. How can you prove that an approximation of a differentiable function is semi-monotonic?

      3. Can you think of an approximation of sine or any other differentiable function that closely represents the actual function, but the derivative of that approximation does not represent the derivative of the actual function's derivative?







      functions trigonometry approximation monotone-functions






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Nov 15 at 5:19









      Deoxal

      84




      84



























          active

          oldest

          votes











          Your Answer





          StackExchange.ifUsing("editor", function () {
          return StackExchange.using("mathjaxEditing", function () {
          StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
          StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
          });
          });
          }, "mathjax-editing");

          StackExchange.ready(function() {
          var channelOptions = {
          tags: "".split(" "),
          id: "69"
          };
          initTagRenderer("".split(" "), "".split(" "), channelOptions);

          StackExchange.using("externalEditor", function() {
          // Have to fire editor after snippets, if snippets enabled
          if (StackExchange.settings.snippets.snippetsEnabled) {
          StackExchange.using("snippets", function() {
          createEditor();
          });
          }
          else {
          createEditor();
          }
          });

          function createEditor() {
          StackExchange.prepareEditor({
          heartbeatType: 'answer',
          convertImagesToLinks: true,
          noModals: true,
          showLowRepImageUploadWarning: true,
          reputationToPostImages: 10,
          bindNavPrevention: true,
          postfix: "",
          imageUploader: {
          brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
          contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
          allowUrls: true
          },
          noCode: true, onDemand: true,
          discardSelector: ".discard-answer"
          ,immediatelyShowMarkdownHelp:true
          });


          }
          });














           

          draft saved


          draft discarded


















          StackExchange.ready(
          function () {
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2999255%2fwhat-does-it-mean-for-a-function-to-be-semi-monotonic%23new-answer', 'question_page');
          }
          );

          Post as a guest















          Required, but never shown






























          active

          oldest

          votes













          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes
















           

          draft saved


          draft discarded



















































           


          draft saved


          draft discarded














          StackExchange.ready(
          function () {
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2999255%2fwhat-does-it-mean-for-a-function-to-be-semi-monotonic%23new-answer', 'question_page');
          }
          );

          Post as a guest















          Required, but never shown





















































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown

































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown







          Popular posts from this blog

          AnyDesk - Fatal Program Failure

          How to calibrate 16:9 built-in touch-screen to a 4:3 resolution?

          QoS: MAC-Priority for clients behind a repeater