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April 18th, 2017, 11:36 AM   #1
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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.
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April 18th, 2017, 12:11 PM   #2
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Quote:
Originally Posted by calypso View Post
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.
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April 18th, 2017, 01:10 PM   #3
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You need to investigate local maxima, discontinuities including vertical asymptotes, and behaviour as $x \to \pm \infty$.
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April 19th, 2017, 04:12 AM   #4
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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 ".
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April 20th, 2017, 12:08 PM   #5
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Thanks for all the responses
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