[MUG] maximize

[MUG] Re: maximize
Author: Maple User Group    Posted: Fri, 15 Nov 2002 10:48:40 -0500
>> From: Maple User Group "maple_gr" | >> From: "Dragomir Deltchev" "Dragomir.Deltchev" | Could someone be so nice to explain me why I cant find the maximum of | -cos(2*t)-t*sin(2*t)+1 | with | maximize(-cos(2*t)-t*sin(2*t)+1,t=0..Pi); -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Mon, 11 Nov 2002 16:29:51 -0800 (PST) From: Robert Israel "israel" To: "Maple-List (E-Mail)" "maple-list" Subject: maximize Ultimately maximize is based on the standard first-year calculus method: candidates for the maximum are the endpoints and the zeros of the derivative. In this case solve can't find the zeros of the derivative (except for 0). This is because AFAIK there is no "closed-form" expression for the maximum. You might try gmax from my Maple Advisor Database <http://www.math.ubc.ca/~israel/advisor>. > gmax(-cos(2*t) + t*sin(2*t) + 1, t = 0 .. Pi); 3.410286238 Robert Israel "israel" Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- From: "Daniel Willard" "willardd" To: "maple-list" Subject: maximize Date: Mon, 11 Nov 2002 20:59:05 -0500 Have you tried plotting it? -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Tue, 12 Nov 2002 14:07:34 +0100 From: Preben Alsholm "P.K.Alsholm" To: "maple-list" Subject: maximize Maple cannot solve tan(z)=z which is necessary in order to find the maximum. So maximize ought to return unevaluated according to the help page (which talks about minimize): "If minimize cannot find the infimum, it returns an unevaluated function call." This deficiency has been known for quite some time. You can find a numerical approximation by using infnorm from the numapprox-package: numapprox[infnorm](-cos(2*t)-t*sin(2*t)+1,t=0..Pi,'pt'); 3.410286238 > pt; 2.246703359 Preben Alsholm Department of Mathematics Technical University of Denmark -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Mon, 11 Nov 2002 12:22:43 -0400 From: C W "sylvester7" To: "maple-list" Subject: maximize Hi ! "maximize" function looks for explicit solutions. That is in this case it finds local extrema by fsolving x-tan(x) and finds 1 value (what version do You have ?) and so Your result follows... This example is best solved manually Chris

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