I would like to thank my calc instructor. <3
Imagine a 2-d plane of x/y axis. Imagine a curve designating your performance in life designated by the function f(x). When someone says you're best they are referring to the point of f(x) where your y value is the global maximum. Which is impossible to have a striaght line curve defining your output. Now say your actual performance is denoted by funtion g(x). Assuming you do absolutely to the best of your raw potential your achievement in life would be denoted by the integral between 0 - infinity (your death) as the area under curve f(x). Now the best you can do it maximize the distance that your g(x) actual output is to f(x). So how much of your best is denoted by the area between the two function denoted by the integral of 0 to infinity of the f(x) - g(x). So all you really have to do is try to minimize the distance between the two curve and reduce the area between. Them. See? Now you know what to say anyone says you're not doing your best.
Good luck on finals guys!
Edit: Of course you can also calculate how far you are from your max potential at point x by taking the limit as that point reaches (delta x) reaches 0 (finding the slope of the tangent line) at that instantaneous moment ala the derivative.
Imagine a 2-d plane of x/y axis. Imagine a curve designating your performance in life designated by the function f(x). When someone says you're best they are referring to the point of f(x) where your y value is the global maximum. Which is impossible to have a striaght line curve defining your output. Now say your actual performance is denoted by funtion g(x). Assuming you do absolutely to the best of your raw potential your achievement in life would be denoted by the integral between 0 - infinity (your death) as the area under curve f(x). Now the best you can do it maximize the distance that your g(x) actual output is to f(x). So how much of your best is denoted by the area between the two function denoted by the integral of 0 to infinity of the f(x) - g(x). So all you really have to do is try to minimize the distance between the two curve and reduce the area between. Them. See? Now you know what to say anyone says you're not doing your best.
Good luck on finals guys!
Edit: Of course you can also calculate how far you are from your max potential at point x by taking the limit as that point reaches (delta x) reaches 0 (finding the slope of the tangent line) at that instantaneous moment ala the derivative.
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