MaplePrimes - comments on Post, Using extrema

MaplePrimes - comments on Post, Using extrema http://www.mapleprimes.com/posts/37995-Using-Extrema en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Thu, 11 Jun 2026 02:48:57 GMT Thu, 11 Jun 2026 02:48:57 GMT The latest comments added to the Post, Using extrema http://www.mapleprimes.com/images/mapleprimeswhite.jpg MaplePrimes - comments on Post, Using extrema http://www.mapleprimes.com/posts/37995-Using-Extrema This might be what you are http://www.mapleprimes.com/posts/37995-Using-Extrema?ref=Feed:MaplePrimes:Using extrema:Comments#comment67823 This might be what you are looking for: <pre> > restart; with(Student[Calculus1]); f := proc (x) options operator, arrow; 3*x^4-4*x^3 end proc; 4 3 f := x -> 3 x - 4 x > ExtremePoints(f(x), x = -1 .. 2); map(f, %); [-1, 1, 2] [7, -1, 16] > plot(f, -1 .. 2); </pre> <a href='http://www.mapleprimes.com/viewfile/3147'><img src='http://www.mapleprimes.com/files/97_extrema.jpeg' alt='97_extrema.jpeg'></a> Regards, --Jean-Marc The latest comments added to the Post, Using extrema 67823 Tue, 27 Jan 2009 11:00:25 Z gulliet gulliet ExtremePoints http://www.mapleprimes.com/posts/37995-Using-Extrema?ref=Feed:MaplePrimes:Using extrema:Comments#comment67824 <pre> Student:-Calculus1:-ExtremePoints(3*x^4 - 4*x^3,-1..2); [-1, 1, 2] </pre> However, that answer is wrong if you need global extrema. The function has a minimum at x=1 and a maximum at x=2 on this interval, which can be found by evaluating <pre> map(x->3*x^4-4*x^3,%); [7, -1, 16] </pre> Alec The latest comments added to the Post, Using extrema 67824 Tue, 27 Jan 2009 11:04:18 Z alec alec Request for a simpler answer http://www.mapleprimes.com/posts/37995-Using-Extrema?ref=Feed:MaplePrimes:Using extrema:Comments#comment67822       <span style="font-size: 14pt; font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: 'Times New Roman'; mso-text-raise: -3.5pt; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA">I don't want to appear ungrateful, but I was hoping for a simpler answer.  For example, <span style="font-size: 14pt; font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: 'Times New Roman'; mso-text-raise: -3.5pt; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"> extrema(3*x^4-4*x^3,{},x);   yields               {-1, 0}   It would be nice if this command could be modified to consider the endpoints.       <span style="font-size: 14pt; font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: 'Times New Roman'; mso-text-raise: -3.5pt; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><v:shape id="_x0000_i1025" style="width: 42pt; height: 15pt" type="#_x0000_t75"><v:imagedata o:title="" src="file:///C:/DOCUME~1/Owner/LOCALS~1/Temp/msoclip1/01/clip_image001.wmz"></v:imagedata></v:shape>   The latest comments added to the Post, Using extrema 67822 Tue, 27 Jan 2009 11:36:24 Z alla alla minimize, maximize http://www.mapleprimes.com/posts/37995-Using-Extrema?ref=Feed:MaplePrimes:Using extrema:Comments#comment82269 If ExtremePoints are too complicated, one can use minimize and maximize. For example, <pre> f:=3*x^4-4*x^3: (minimize,maximize)(f,x=-1..2,location); -1, {[{x = 1}, -1]}, 16, {[{x = 2}, 16]} </pre> But that may be erroneous in cases with several local minimums and maximums (as well as ExtremePoints). So it is always a good idea to look at the plot at least. Alec The latest comments added to the Post, Using extrema 82269 Tue, 27 Jan 2009 12:08:00 Z alec alec