Para hallar los extremos hay que resolver la ecuación
dxdf(x)=0(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
dxdf(x)=primera derivadacos(x)sign(sin(x))=0Resolvermos esta ecuaciónRaíces de esta ecuación
x1=−2279.22547017939x2=32.9867228626928x3=73.8274273593601x4=4.71238898038469x5=39.2699081698724x6=95.8185759344887x7=45.553093477052x8=70.6858347057703x9=−10.9955742875643x10=−58.1194640914112x11=−23.5619449019235x12=26.7035375555132x13=−26.7035375555132x14=−89.5353906273091x15=−17.2787595947439x16=−42.4115008234622x17=−61.261056745001x18=92.6769832808989x19=−76.9690200129499x20=−92.6769832808989x21=−98.9601685880785x22=61.261056745001x23=−54.9778714378214x24=42.4115008234622x25=−64.4026493985908x26=67.5442420521806x27=−7.85398163397448x28=80.1106126665397x29=−14.1371669411541x30=14.1371669411541x31=−1.5707963267949x32=1.5707963267949x33=29.845130209103x34=10.9955742875643x35=17.2787595947439x36=−51.8362787842316x37=−29.845130209103x38=0x39=−183.783170235003x40=−48.6946861306418x41=−73.8274273593601x42=23.5619449019235x43=20.4203522483337x44=−86.3937979737193x45=54.9778714378214x46=58.1194640914112x47=51.8362787842316x48=−67.5442420521806x49=237.190245346029x50=−4.71238898038469x51=−70.6858347057703x52=−45.553093477052x53=48.6946861306418x54=−83.2522053201295x55=−95.8185759344887x56=89.5353906273091x57=−39.2699081698724x58=−306.305283725005x59=76.9690200129499x60=−32.9867228626928x61=−20.4203522483337x62=−36.1283155162826x63=7.85398163397448x64=−80.1106126665397x65=86.3937979737193x66=98.9601685880785x67=36.1283155162826x68=64.4026493985908x69=83.2522053201295Signos de extremos en los puntos:
(-2279.225470179395, 1)
(32.98672286269283, 1)
(73.82742735936014, 1)
(4.71238898038469, 1)
(39.269908169872416, 1)
(95.81857593448869, 1)
(45.553093477052, 1)
(70.68583470577035, 1)
(-10.995574287564276, 1)
(-58.119464091411174, 1)
(-23.56194490192345, 1)
(26.703537555513243, 1)
(-26.703537555513243, 1)
(-89.53539062730911, 1)
(-17.278759594743864, 1)
(-42.411500823462205, 1)
(-61.26105674500097, 1)
(92.6769832808989, 1)
(-76.96902001294994, 1)
(-92.6769832808989, 1)
(-98.96016858807849, 1)
(61.26105674500097, 1)
(-54.977871437821385, 1)
(42.411500823462205, 1)
(-64.40264939859077, 1)
(67.54424205218055, 1)
(-7.853981633974483, 1)
(80.11061266653972, 1)
(-14.137166941154069, 1)
(14.137166941154069, 1)
(-1.5707963267948966, 1)
(1.5707963267948966, 1)
(29.845130209103036, 1)
(10.995574287564276, 1)
(17.278759594743864, 1)
(-51.83627878423159, 1)
(-29.845130209103036, 1)
(0, 0)
(-183.7831702350029, 1)
(-48.6946861306418, 1)
(-73.82742735936014, 1)
(23.56194490192345, 1)
(20.420352248333657, 1)
(-86.39379797371932, 1)
(54.977871437821385, 1)
(58.119464091411174, 1)
(51.83627878423159, 1)
(-67.54424205218055, 1)
(237.1902453460294, 1)
(-4.71238898038469, 1)
(-70.68583470577035, 1)
(-45.553093477052, 1)
(48.6946861306418, 1)
(-83.25220532012952, 1)
(-95.81857593448869, 1)
(89.53539062730911, 1)
(-39.269908169872416, 1)
(-306.3052837250048, 1)
(76.96902001294994, 1)
(-32.98672286269283, 1)
(-20.420352248333657, 1)
(-36.12831551628262, 1)
(7.853981633974483, 1)
(-80.11061266653972, 1)
(86.39379797371932, 1)
(98.96016858807849, 1)
(36.12831551628262, 1)
(64.40264939859077, 1)
(83.25220532012952, 1)
Intervalos de crecimiento y decrecimiento de la función:Hallemos los intervalos donde la función crece y decrece y también los puntos mínimos y máximos de la función, para lo cual miramos cómo se comporta la función en los extremos con desviación mínima del extremo:
Puntos mínimos de la función:
x1=0Puntos máximos de la función:
x1=−2279.22547017939x1=32.9867228626928x1=73.8274273593601x1=4.71238898038469x1=39.2699081698724x1=95.8185759344887x1=45.553093477052x1=70.6858347057703x1=−10.9955742875643x1=−58.1194640914112x1=−23.5619449019235x1=26.7035375555132x1=−26.7035375555132x1=−89.5353906273091x1=−17.2787595947439x1=−42.4115008234622x1=−61.261056745001x1=92.6769832808989x1=−76.9690200129499x1=−92.6769832808989x1=−98.9601685880785x1=61.261056745001x1=−54.9778714378214x1=42.4115008234622x1=−64.4026493985908x1=67.5442420521806x1=−7.85398163397448x1=80.1106126665397x1=−14.1371669411541x1=14.1371669411541x1=−1.5707963267949x1=1.5707963267949x1=29.845130209103x1=10.9955742875643x1=17.2787595947439x1=−51.8362787842316x1=−29.845130209103x1=−183.783170235003x1=−48.6946861306418x1=−73.8274273593601x1=23.5619449019235x1=20.4203522483337x1=−86.3937979737193x1=54.9778714378214x1=58.1194640914112x1=51.8362787842316x1=−67.5442420521806x1=237.190245346029x1=−4.71238898038469x1=−70.6858347057703x1=−45.553093477052x1=48.6946861306418x1=−83.2522053201295x1=−95.8185759344887x1=89.5353906273091x1=−39.2699081698724x1=−306.305283725005x1=76.9690200129499x1=−32.9867228626928x1=−20.4203522483337x1=−36.1283155162826x1=7.85398163397448x1=−80.1106126665397x1=86.3937979737193x1=98.9601685880785x1=36.1283155162826x1=64.4026493985908x1=83.2522053201295Decrece en los intervalos
(−∞,−2279.22547017939]∪[0,∞)Crece en los intervalos
(−∞,0]∪[237.190245346029,∞)