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











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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?










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    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






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      asked Nov 15 at 5:19









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