April 18th, 2017, 12:36 PM  #1 
Senior Member Joined: Feb 2015 From: london Posts: 121 Thanks: 0  Calculate Supremum of function
f(x) = 12 (x^2  x +0.25), (0 < x < 1) I can plot this function between 0 and 1 in excel and i can see that the supremum are at x,y coords 0,3, and 1,3. Apart from always ploting the function is there any other way I can find the supremum of a function. For example to find mimumum/maximum of function I can differentiate and equate to 0. 
April 18th, 2017, 01:11 PM  #2  
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,601 Thanks: 816  Quote:
 
April 18th, 2017, 02:10 PM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,031 Thanks: 2342 Math Focus: Mainly analysis and algebra 
You need to investigate local maxima, discontinuities including vertical asymptotes, and behaviour as $x \to \pm \infty$.

April 19th, 2017, 05:12 AM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,820 Thanks: 750 
Did you not notice that this is a perfect square? . That has its minimum at, 0, x= 1/2. The maximum must be at one or both of the endpoints. Calculate the value at x= 0 and x= 1. Since this function is only defined between 0 and 1, there is no point is determining "the behavior as ". 
April 20th, 2017, 01:08 PM  #5 
Senior Member Joined: Feb 2015 From: london Posts: 121 Thanks: 0 
Thanks for all the responses


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