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 April 18th, 2017, 11:36 AM #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 co-ords 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, 12:11 PM   #2
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 Originally Posted by calypso 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 co-ords 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.
of a general function? Not really. Finding critical points only gives you local minima or maxima. They say nothing about the global behavior of the function.

 April 18th, 2017, 01:10 PM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,214 Thanks: 2410 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, 04:12 AM #4 Math Team   Joined: Jan 2015 From: Alabama Posts: 2,966 Thanks: 807 Did you not notice that this is a perfect square? $12(x^2- x+ 1/4)= 12(x- 1/2)^2$. 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 $x\to \pm\infty$".
 April 20th, 2017, 12:08 PM #5 Senior Member   Joined: Feb 2015 From: london Posts: 121 Thanks: 0 Thanks for all the responses

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