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tan(2)^(6)*x*cos(7*x)^2
Trazado el gráfico de la función/ tan(2)^(6)*x*cos(7*x)^2

Gráfico de la función y = tan(2)^(6)*x*cos(7*x)^2

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
          6         2     
f(x) = tan (2)*x*cos (7*x)
f(x)=xtan⁡6(2)cos⁡2(7x)f{\left(x \right)} = x \tan^{6}{\left(2 \right)} \cos^{2}{\left(7 x \right)} 
f = (x*tan(2)^6)*cos(7*x)^2
Gráfico de la función
02468-8-6-4-2-1010-25002500
Puntos de cruce con el eje de coordenadas X
El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
xtan⁡6(2)cos⁡2(7x)=0x \tan^{6}{\left(2 \right)} \cos^{2}{\left(7 x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=0x_{1} = 0
x2=−π2x_{2} = - \frac{\pi}{2}
x3=−3π14x_{3} = - \frac{3 \pi}{14}
x4=−π14x_{4} = - \frac{\pi}{14}
x5=π14x_{5} = \frac{\pi}{14}
x6=3π14x_{6} = \frac{3 \pi}{14}
x7=π2x_{7} = \frac{\pi}{2}
x8=11π14x_{8} = \frac{11 \pi}{14}
x9=13π14x_{9} = \frac{13 \pi}{14}
x10=−ilog⁡(−−114)x_{10} = - i \log{\left(- \sqrt[14]{-1} \right)}
x11=−ilog⁡(−(−1)314)x_{11} = - i \log{\left(- \left(-1\right)^{\frac{3}{14}} \right)}
Solución numérica
x1=0x_{1} = 0
x2=−1.5707963267949x_{2} = -1.5707963267949
x3=−0.673198425769241x_{3} = -0.673198425769241
x4=−0.224399475256414x_{4} = -0.224399475256414
x5=0.224399475256414x_{5} = 0.224399475256414
x6=0.673198425769241x_{6} = 0.673198425769241
x7=1.5707963267949x_{7} = 1.5707963267949
x8=2.46839422782055x_{8} = 2.46839422782055
x9=2.91719317833338x_{9} = 2.91719317833338
x10=−2.01959527730772x_{10} = -2.01959527730772
x11=2.01959527730772x_{11} = 2.01959527730772
x12=−1.12199737628207x_{12} = -1.12199737628207
x13=1.12199737628207x_{13} = 1.12199737628207
Puntos de cruce con el eje de coordenadas Y
El gráfico cruce el eje Y cuando x es igual a 0:
sustituimos x = 0 en (tan(2)^6*x)*cos(7*x)^2.
0tan⁡6(2)cos⁡2(0⋅7)0 \tan^{6}{\left(2 \right)} \cos^{2}{\left(0 \cdot 7 \right)}
Resultado:
f(0)=0f{\left(0 \right)} = 0
Punto:
(0, 0)
Extremos de la función
Para hallar los extremos hay que resolver la ecuación
ddxf(x)=0\frac{d}{d x} f{\left(x \right)} = 0
(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
ddxf(x)=\frac{d}{d x} f{\left(x \right)} =
primera derivada
−14xsin⁡(7x)cos⁡(7x)tan⁡6(2)+cos⁡2(7x)tan⁡6(2)=0- 14 x \sin{\left(7 x \right)} \cos{\left(7 x \right)} \tan^{6}{\left(2 \right)} + \cos^{2}{\left(7 x \right)} \tan^{6}{\left(2 \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−9.87461025876599x_{1} = -9.87461025876599
x2=−19.7476705436182x_{2} = -19.7476705436182
x3=96.2673748850015x_{3} = 96.2673748850015
x4=−25.8059396544876x_{4} = -25.8059396544876
x5=38.1481782787015x_{5} = 38.1481782787015
x6=60.1392290429398x_{6} = 60.1392290429398
x7=48.245887180129x_{7} = 48.245887180129
x8=33.211429583558x_{8} = 33.211429583558
x9=−89.5353906273091x_{9} = -89.5353906273091
x10=−41.7385468736615x_{10} = -41.7385468736615
x11=24.0107438524363x_{11} = 24.0107438524363
x12=55.2024557613023x_{12} = 55.2024557613023
x13=62.1586546460266x_{13} = 62.1586546460266
x14=−79.8863409237441x_{14} = -79.8863409237441
x15=−75.8471571714217x_{15} = -75.8471571714217
x16=−53.856063530932x_{16} = -53.856063530932
x17=14.1371669411541x_{17} = 14.1371669411541
x18=64.1784089188219x_{18} = 64.1784089188219
x19=74.276226309873x_{19} = 74.276226309873
x20=−11.8931721885899x_{20} = -11.8931721885899
x21=52.2850777347444x_{21} = 52.2850777347444
x22=71.583432606796x_{22} = 71.583432606796
x23=−3.14483680523185x_{23} = -3.14483680523185
x24=12.1184136852306x_{24} = 12.1184136852306
x25=−9.20037848551297x_{25} = -9.20037848551297
x26=40.1675060708981x_{26} = 40.1675060708981
x27=36.1283155162826x_{27} = 36.1283155162826
x28=42.1873432234011x_{28} = 42.1873432234011
x29=−1.80085906346792x_{29} = -1.80085906346792
x30=2.24853133657212x_{30} = 2.24853133657212
x31=−39.7187071203852x_{31} = -39.7187071203852
x32=−46.0018924275648x_{32} = -46.0018924275648
x33=16.1573937568963x_{33} = 16.1573937568963
x34=−27.8259016426157x_{34} = -27.8259016426157
x35=−61.7098556955138x_{35} = -61.7098556955138
x36=−29.845130209103x_{36} = -29.845130209103
x37=−33.8843207637185x_{37} = -33.8843207637185
x38=0.0933244552992004x_{38} = 0.0933244552992004
x39=−31.8650457139301x_{39} = -31.8650457139301
x40=−17.7275585452567x_{40} = -17.7275585452567
x41=86.1695169171295x_{41} = 86.1695169171295
x42=−93.7990894437344x_{42} = -93.7990894437344
x43=−69.7882368047447x_{43} = -69.7882368047447
x44=−82.1303321863628x_{44} = -82.1303321863628
x45=−65.7490462501292x_{45} = -65.7490462501292
x46=−0.224399475256414x_{46} = -0.224399475256414
x47=−63.7296110879891x_{47} = -63.7296110879891
x48=−87.7401948252578x_{48} = -87.7401948252578
x49=−15.708612848622x_{49} = -15.708612848622
x50=20.1964580121188x_{50} = 20.1964580121188
x51=66.1978452006421x_{51} = 66.1978452006421
x52=−51.8362787842316x_{52} = -51.8362787842316
x53=−47.7970882296161x_{53} = -47.7970882296161
x54=−92.0038957643417x_{54} = -92.0038957643417
x55=−71.8079741843521x_{55} = -71.8079741843521
x56=−35.9042002436571x_{56} = -35.9042002436571
x57=−85.7207185866077x_{57} = -85.7207185866077
x58=98.2870739814527x_{58} = 98.2870739814527
x59=58.1194640914112x_{59} = 58.1194640914112
x60=88.1889937757706x_{60} = 88.1889937757706
x61=0.470330003040298x_{61} = 0.470330003040298
x62=−0.0933244552992004x_{62} = -0.0933244552992004
x63=94.2478878762175x_{63} = 94.2478878762175
x64=90.2087021694325x_{64} = 90.2087021694325
x65=−95.8185759344887x_{65} = -95.8185759344887
x66=−99.8577664891041x_{66} = -99.8577664891041
x67=18.1763574957695x_{67} = 18.1763574957695
x68=−23.7867733572188x_{68} = -23.7867733572188
x69=−97.8382755071733x_{69} = -97.8382755071733
x70=6.28480884777756x_{70} = 6.28480884777756
x71=−49.8168883385579x_{71} = -49.8168883385579
x72=28.2746947724966x_{72} = 28.2746947724966
x73=−57.89524086685x_{73} = -57.89524086685
x74=82.1303321863628x_{74} = 82.1303321863628
x75=−55.875469338847x_{75} = -55.875469338847
x76=−7.85398163397448x_{76} = -7.85398163397448
x77=72.256772252246x_{77} = 72.256772252246
x78=80.1106126665397x_{78} = 80.1106126665397
x79=84.1498032211552x_{79} = 84.1498032211552
x80=76.5202210624371x_{80} = 76.5202210624371
x81=26.2547386050004x_{81} = 26.2547386050004
x82=−5.83613470085334x_{82} = -5.83613470085334
x83=4.26359002987186x_{83} = 4.26359002987186
x84=−73.8274273593601x_{84} = -73.8274273593601
x85=92.4526941764618x_{85} = 92.4526941764618
x86=50.2656854602341x_{86} = 50.2656854602341
x87=56.100050704779x_{87} = 56.100050704779
x88=−3.81479107935903x_{88} = -3.81479107935903
x89=44.2066966255135x_{89} = 44.2066966255135
x90=30.2939291596159x_{90} = 30.2939291596159
x91=34.1090193993406x_{91} = 34.1090193993406
x92=10.0979763865386x_{92} = 10.0979763865386
x93=−77.8666179139756x_{93} = -77.8666179139756
Signos de extremos en los puntos:
                                          6    
(-9.874610258765987, -9.87409360304636*tan (2))

                                          6    
(-19.74767054361817, -19.7474121853447*tan (2))

                                            6    
(96.26737488500152, 8.78839398920626e-25*tan (2))

                                               6    
(-25.805939654487588, -7.50489962228377e-28*tan (2))

                                        6    
(38.14817827870152, 38.1480445364585*tan (2))

                                        6    
(60.13922904293982, 60.1391442059091*tan (2))

                                            6    
(48.24588718012897, 2.34503295865519e-26*tan (2))

                                        6    
(33.21142958355798, 33.2112759612273*tan (2))

                                              6    
(-89.53539062730911, -3.91939002728315e-25*tan (2))

                                          6    
(-41.73854687366148, -41.7384246359159*tan (2))

                                             6    
(24.010743852436278, 1.66536603249196e-27*tan (2))

                                        6    
(55.20245576130234, 55.2023633372932*tan (2))

                                             6    
(62.158654646026626, 1.07871605619822e-25*tan (2))

                                          6    
(-79.88634092374414, -79.8862770575478*tan (2))

                                          6    
(-75.84715717142166, -75.8470899040845*tan (2))

                                        6    
(-53.856063530932, -53.8559687963468*tan (2))

                                             6    
(14.137166941154069, 3.06085974379874e-29*tan (2))

                                        6    
(64.17840891882194, 64.1783294211438*tan (2))

                                          6    
(74.27622630987297, 3.609449200233e-26*tan (2))

                                               6    
(-11.893172188589931, -2.56635054906443e-29*tan (2))

                                            6    
(52.28507773474442, 1.38447369493553e-25*tan (2))

                                            6    
(71.58343260679601, 1.30146993039844e-25*tan (2))

                                           6    
(-3.1448368052318516, -3.14321528702457*tan (2))

                                         6    
(12.118413685230559, 12.1179926842893*tan (2))

                                              6    
(-9.200378485512966, -5.65448569364571e-28*tan (2))

                                            6    
(40.16750607089807, 8.72602038708157e-29*tan (2))

                                            6    
(36.12831551628262, 8.33333793772587e-27*tan (2))

                                         6    
(42.187343223401115, 42.1872222860346*tan (2))

                                          6    
(-1.800859063467916, -1.79803039853426*tan (2))

                                         6    
(2.2485313365721242, 2.24626456923199*tan (2))

                                              6    
(-39.71870712038524, -7.89675566599354e-26*tan (2))

                                              6    
(-46.00189242756483, -4.66837920492084e-26*tan (2))

                                        6    
(16.15739375689631, 16.1570779917931*tan (2))

                                          6    
(-27.825901642615715, -27.825718288011*tan (2))

                                               6    
(-61.709855695513795, -1.19709102156758e-27*tan (2))

                                              6    
(-29.845130209103036, -1.2100893490981e-27*tan (2))

                                               6    
(-33.884320763718485, -3.59049041614397e-27*tan (2))

                                            6    
(0.09332445529920044, 0.0588498971202244*tan (2))

                                           6    
(-31.865045713930073, -31.8648856007068*tan (2))

                                              6    
(-17.72755854525669, -4.28624518877433e-30*tan (2))

                                        6    
(86.16951691712951, 86.1694577078233*tan (2))

                                          6    
(-93.79908944373445, -93.7990350504787*tan (2))

                                             6    
(-69.7882368047447, -5.83619849852646e-26*tan (2))

                                          6    
(-82.13033218636284, -82.1302700651365*tan (2))

                                              6    
(-65.74904625012924, -1.30705788845543e-25*tan (2))

                                               6    
(-0.2243994752564138, -8.41363270599985e-34*tan (2))

                                          6    
(-63.72961108798911, -63.7295310304724*tan (2))

                                             6    
(-87.7401948252578, -1.70013271407891e-27*tan (2))

                                           6    
(-15.708612848622005, -15.7082880627623*tan (2))

                                         6    
(20.196458012118764, 20.1962053947045*tan (2))

                                            6    
(66.19784520064208, 2.25152079060782e-25*tan (2))

                                              6    
(-51.83627878423159, -1.50889048851708e-27*tan (2))

                                              6    
(-47.79708822961614, -9.92883711869596e-26*tan (2))

                                          6    
(-92.00389576434168, -92.0038403097579*tan (2))

                                         6    
(-71.8079741843521, -71.8079031332491*tan (2))

                                           6    
(-35.904200243657144, -35.9040581427166*tan (2))

                                          6    
(-85.72071858660769, -85.7206590673064*tan (2))

                                        6    
(98.28707398145274, 98.2870220718993*tan (2))

                                             6    
(58.119464091411174, 3.63160384824741e-26*tan (2))

                                            6    
(88.18899377577063, 2.03283636195362e-26*tan (2))

                                          6    
(0.4703300030402981, 0.459726768858255*tan (2))

                                              6    
(-0.09332445529920044, -0.0588498971202244*tan (2))

                                        6    
(94.24788787621746, 94.2478337419764*tan (2))

                                        6    
(90.20870216943248, 90.2086456112791*tan (2))

                                              6    
(-95.81857593448869, -8.01441641500049e-26*tan (2))

                                              6    
(-99.85776648910414, -4.63163922232588e-25*tan (2))

                                            6    
(18.17635749576952, 2.79585219288648e-28*tan (2))

                                           6    
(-23.786773357218845, -23.7865588684887*tan (2))

                                          6    
(-97.83827550717332, -97.8382233595034*tan (2))

                                        6    
(6.284808847777558, 6.28399714737469*tan (2))

                                          6    
(-49.81688833855788, -49.8167859228812*tan (2))

                                        6    
(28.27469477249662, 28.2745143281701*tan (2))

                                           6    
(-57.895240866850024, -57.8951527415918*tan (2))

                                        6    
(82.13033218636284, 82.1302700651365*tan (2))

                                              6    
(-55.87546933884704, -2.71831594338562e-26*tan (2))

                                              6    
(-7.853981633974483, -1.20655944359504e-28*tan (2))

                                        6    
(72.25677225224598, 72.2567016424516*tan (2))

                                            6    
(80.11061266653972, 1.88481359874362e-25*tan (2))

                                            6    
(84.14980322115518, 5.63657643207218e-25*tan (2))

                                           6    
(76.5202210624371, 4.41367934949078e-25*tan (2))

                                             6    
(26.254738605000416, 7.62140381506604e-28*tan (2))

                                          6    
(-5.836134700853338, -5.83526061604565*tan (2))

                                            6    
(4.263590029871862, 3.68470334815878e-29*tan (2))

                                              6    
(-73.82742735936014, -9.36648117450064e-27*tan (2))

                                        6    
(92.45269417646178, 92.4526389910741*tan (2))

                                         6    
(50.265685460234145, 50.2655839589721*tan (2))

                                        6    
(56.10005070477896, 56.0999597595395*tan (2))

                                               6    
(-3.8147910793590345, -2.06312883147019e-30*tan (2))

                                             6    
(44.206696625513516, 6.62357259545183e-26*tan (2))

                                             6    
(30.293929159615864, 3.85015058508972e-27*tan (2))

                                        6    
(34.109019399340575, 34.108869819595*tan (2))

                                            6    
(10.09797638653862, 9.68026139285446e-30*tan (2))

                                              6    
(-77.86661791397559, -2.26868252765451e-27*tan (2))


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=−9.87461025876599x_{1} = -9.87461025876599
x2=−19.7476705436182x_{2} = -19.7476705436182
x3=96.2673748850015x_{3} = 96.2673748850015
x4=48.245887180129x_{4} = 48.245887180129
x5=−41.7385468736615x_{5} = -41.7385468736615
x6=24.0107438524363x_{6} = 24.0107438524363
x7=62.1586546460266x_{7} = 62.1586546460266
x8=−79.8863409237441x_{8} = -79.8863409237441
x9=−75.8471571714217x_{9} = -75.8471571714217
x10=−53.856063530932x_{10} = -53.856063530932
x11=14.1371669411541x_{11} = 14.1371669411541
x12=74.276226309873x_{12} = 74.276226309873
x13=52.2850777347444x_{13} = 52.2850777347444
x14=71.583432606796x_{14} = 71.583432606796
x15=−3.14483680523185x_{15} = -3.14483680523185
x16=40.1675060708981x_{16} = 40.1675060708981
x17=36.1283155162826x_{17} = 36.1283155162826
x18=−1.80085906346792x_{18} = -1.80085906346792
x19=−27.8259016426157x_{19} = -27.8259016426157
x20=−31.8650457139301x_{20} = -31.8650457139301
x21=−93.7990894437344x_{21} = -93.7990894437344
x22=−82.1303321863628x_{22} = -82.1303321863628
x23=−63.7296110879891x_{23} = -63.7296110879891
x24=−15.708612848622x_{24} = -15.708612848622
x25=66.1978452006421x_{25} = 66.1978452006421
x26=−92.0038957643417x_{26} = -92.0038957643417
x27=−71.8079741843521x_{27} = -71.8079741843521
x28=−35.9042002436571x_{28} = -35.9042002436571
x29=−85.7207185866077x_{29} = -85.7207185866077
x30=58.1194640914112x_{30} = 58.1194640914112
x31=88.1889937757706x_{31} = 88.1889937757706
x32=−0.0933244552992004x_{32} = -0.0933244552992004
x33=18.1763574957695x_{33} = 18.1763574957695
x34=−23.7867733572188x_{34} = -23.7867733572188
x35=−97.8382755071733x_{35} = -97.8382755071733
x36=−49.8168883385579x_{36} = -49.8168883385579
x37=−57.89524086685x_{37} = -57.89524086685
x38=80.1106126665397x_{38} = 80.1106126665397
x39=84.1498032211552x_{39} = 84.1498032211552
x40=76.5202210624371x_{40} = 76.5202210624371
x41=26.2547386050004x_{41} = 26.2547386050004
x42=−5.83613470085334x_{42} = -5.83613470085334
x43=4.26359002987186x_{43} = 4.26359002987186
x44=44.2066966255135x_{44} = 44.2066966255135
x45=30.2939291596159x_{45} = 30.2939291596159
x46=10.0979763865386x_{46} = 10.0979763865386
Puntos máximos de la función:
x46=−25.8059396544876x_{46} = -25.8059396544876
x46=38.1481782787015x_{46} = 38.1481782787015
x46=60.1392290429398x_{46} = 60.1392290429398
x46=33.211429583558x_{46} = 33.211429583558
x46=−89.5353906273091x_{46} = -89.5353906273091
x46=55.2024557613023x_{46} = 55.2024557613023
x46=64.1784089188219x_{46} = 64.1784089188219
x46=−11.8931721885899x_{46} = -11.8931721885899
x46=12.1184136852306x_{46} = 12.1184136852306
x46=−9.20037848551297x_{46} = -9.20037848551297
x46=42.1873432234011x_{46} = 42.1873432234011
x46=2.24853133657212x_{46} = 2.24853133657212
x46=−39.7187071203852x_{46} = -39.7187071203852
x46=−46.0018924275648x_{46} = -46.0018924275648
x46=16.1573937568963x_{46} = 16.1573937568963
x46=−61.7098556955138x_{46} = -61.7098556955138
x46=−29.845130209103x_{46} = -29.845130209103
x46=−33.8843207637185x_{46} = -33.8843207637185
x46=0.0933244552992004x_{46} = 0.0933244552992004
x46=−17.7275585452567x_{46} = -17.7275585452567
x46=86.1695169171295x_{46} = 86.1695169171295
x46=−69.7882368047447x_{46} = -69.7882368047447
x46=−65.7490462501292x_{46} = -65.7490462501292
x46=−0.224399475256414x_{46} = -0.224399475256414
x46=−87.7401948252578x_{46} = -87.7401948252578
x46=20.1964580121188x_{46} = 20.1964580121188
x46=−51.8362787842316x_{46} = -51.8362787842316
x46=−47.7970882296161x_{46} = -47.7970882296161
x46=98.2870739814527x_{46} = 98.2870739814527
x46=0.470330003040298x_{46} = 0.470330003040298
x46=94.2478878762175x_{46} = 94.2478878762175
x46=90.2087021694325x_{46} = 90.2087021694325
x46=−95.8185759344887x_{46} = -95.8185759344887
x46=−99.8577664891041x_{46} = -99.8577664891041
x46=6.28480884777756x_{46} = 6.28480884777756
x46=28.2746947724966x_{46} = 28.2746947724966
x46=82.1303321863628x_{46} = 82.1303321863628
x46=−55.875469338847x_{46} = -55.875469338847
x46=−7.85398163397448x_{46} = -7.85398163397448
x46=72.256772252246x_{46} = 72.256772252246
x46=−73.8274273593601x_{46} = -73.8274273593601
x46=92.4526941764618x_{46} = 92.4526941764618
x46=50.2656854602341x_{46} = 50.2656854602341
x46=56.100050704779x_{46} = 56.100050704779
x46=−3.81479107935903x_{46} = -3.81479107935903
x46=34.1090193993406x_{46} = 34.1090193993406
x46=−77.8666179139756x_{46} = -77.8666179139756
Decrece en los intervalos
[96.2673748850015,∞)\left[96.2673748850015, \infty\right)
Crece en los intervalos
(−∞,−97.8382755071733]\left(-\infty, -97.8382755071733\right]
Puntos de flexiones
Hallemos los puntos de flexiones, para eso hay que resolver la ecuación
d2dx2f(x)=0\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0
(la segunda derivada es igual a cero),
las raíces de la ecuación obtenida serán los puntos de flexión para el gráfico de la función indicado:
d2dx2f(x)=\frac{d^{2}}{d x^{2}} f{\left(x \right)} =
segunda derivada
14(7x(sin⁡2(7x)−cos⁡2(7x))−2sin⁡(7x)cos⁡(7x))tan⁡6(2)=014 \left(7 x \left(\sin^{2}{\left(7 x \right)} - \cos^{2}{\left(7 x \right)}\right) - 2 \sin{\left(7 x \right)} \cos{\left(7 x \right)}\right) \tan^{6}{\left(2 \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−75.7349576329835x_{1} = -75.7349576329835
x2=40.2799591364608x_{2} = 40.2799591364608
x3=30.1820675037122x_{3} = 30.1820675037122
x4=62.2710182490294x_{4} = 62.2710182490294
x5=−83.8133257558764x_{5} = -83.8133257558764
x6=22.1038099498946x_{6} = 22.1038099498946
x7=94.1356882675712x_{7} = 94.1356882675712
x8=−7.74309957591203x_{8} = -7.74309957591203
x9=18.2891151539985x_{9} = 18.2891151539985
x10=66.3101988220774x_{10} = 66.3101988220774
x11=90.0965025725999x_{11} = 90.0965025725999
x12=48.1338994355408x_{12} = 48.1338994355408
x13=92.1160953668133x_{13} = 92.1160953668133
x14=10.2111753642745x_{14} = 10.2111753642745
x15=64.2906083787768x_{15} = 64.2906083787768
x16=40.0555610803785x_{16} = 40.0555610803785
x17=26.1429291824741x_{17} = 26.1429291824741
x18=−10.43555335728x_{18} = -10.43555335728
x19=−27.713703387155x_{19} = -27.713703387155
x20=−85.832918168548x_{20} = -85.832918168548
x21=82.2425317543994x_{21} = 82.2425317543994
x22=−80.2229396005895x_{22} = -80.2229396005895
x23=16.2695891273924x_{23} = 16.2695891273924
x24=−33.099230885982x_{24} = -33.099230885982
x25=−53.7438641885171x_{25} = -53.7438641885171
x26=52.1730735780056x_{26} = 52.1730735780056
x27=−97.7260758892311x_{27} = -97.7260758892311
x28=−39.8311630402863x_{28} = -39.8311630402863
x29=4.15384586276036x_{29} = 4.15384586276036
x30=84.2621240579364x_{30} = 84.2621240579364
x31=−59.8026307848198x_{31} = -59.8026307848198
x32=−37.8115814459875x_{32} = -37.8115814459875
x33=−91.8916961620663x_{33} = -91.8916961620663
x34=−31.3040527627982x_{34} = -31.3040527627982
x35=50.1534861763339x_{35} = 50.1534861763339
x36=8.1918263624443x_{36} = 8.1918263624443
x37=79.9985404821234x_{37} = 79.9985404821234
x38=−0.363356078150162x_{38} = -0.363356078150162
x39=0x_{39} = 0
x40=−51.7242763244855x_{40} = -51.7242763244855
x41=−23.8989710771266x_{41} = -23.8989710771266
x42=−99.7456690524054x_{42} = -99.7456690524054
x43=76.1837557897812x_{43} = 76.1837557897812
x44=−41.8507459551568x_{44} = -41.8507459551568
x45=−61.8222204880913x_{45} = -61.8222204880913
x46=72.1445727341044x_{46} = 72.1445727341044
x47=−11.7818384942038x_{47} = -11.7818384942038
x48=65.6370019745912x_{48} = 65.6370019745912
x49=−29.7332736561249x_{49} = -29.7332736561249
x50=−95.7064828152812x_{50} = -95.7064828152812
x51=−63.8418105440214x_{51} = -63.8418105440214
x52=−15.820807966589x_{52} = -15.820807966589
x53=−17.8403302377427x_{53} = -17.8403302377427
x54=−13.8013070580432x_{54} = -13.8013070580432
x55=−69.9005825220923x_{55} = -69.9005825220923
x56=−19.8598673554491x_{56} = -19.8598673554491
x57=54.1926615666706x_{57} = 54.1926615666706
x58=74.1641641598402x_{58} = 74.1641641598402
x59=−45.889915049221x_{59} = -45.889915049221
x60=−89.8721033801316x_{60} = -89.8721033801316
x61=32.2016415780069x_{61} = 32.2016415780069
x62=23.8989710771266x_{62} = 23.8989710771266
x63=86.2817165006867x_{63} = 86.2817165006867
x64=−50.1534861763339x_{64} = -50.1534861763339
x65=−58.0074402633035x_{65} = -58.0074402633035
x66=28.1624964703041x_{66} = 28.1624964703041
x67=−87.8525107129261x_{67} = -87.8525107129261
x68=−3.70534386095906x_{68} = -3.70534386095906
x69=−31.7528471061951x_{69} = -31.7528471061951
x70=88.7501074392409x_{70} = 88.7501074392409
x71=3.48112148535039x_{71} = 3.48112148535039
x72=98.1748743624197x_{72} = 98.1748743624197
x73=−70.7981785723577x_{73} = -70.7981785723577
x74=56.2122500790616x_{74} = 56.2122500790616
x75=70.1249815302169x_{75} = 70.1249815302169
x76=14.2500827265421x_{76} = 14.2500827265421
x77=96.1552812681603x_{77} = 96.1552812681603
x78=−73.7153660469939x_{78} = -73.7153660469939
x79=−94.3600874850462x_{79} = -94.3600874850462
x80=60.2514284643652x_{80} = 60.2514284643652
x81=38.2603772309992x_{81} = 38.2603772309992
x82=−43.8703300082251x_{82} = -43.8703300082251
x83=−81.7937334846673x_{83} = -81.7937334846673
x84=−65.8614009201684x_{84} = -65.8614009201684
x85=−67.8809915879513x_{85} = -67.8809915879513
x86=33.9968206476951x_{86} = 33.9968206476951
x87=−77.7545494107282x_{87} = -77.7545494107282
x88=−21.8794152090433x_{88} = -21.8794152090433
x89=−46.3387118461673x_{89} = -46.3387118461673
x90=46.1143134424544x_{90} = 46.1143134424544
x91=100.194467544685x_{91} = 100.194467544685
x92=−5.72396894243389x_{92} = -5.72396894243389
x93=68.1053905679135x_{93} = 68.1053905679135
x94=6.17263838957976x_{94} = 6.17263838957976
x95=−35.7920013957943x_{95} = -35.7920013957943
x96=24.1233665808737x_{96} = 24.1233665808737
x97=2.13656384782513x_{97} = 2.13656384782513
x98=78.2033476081068x_{98} = 78.2033476081068

Intervalos de convexidad y concavidad:
Hallemos los intervales donde la función es convexa o cóncava, para eso veamos cómo se comporta la función en los puntos de flexiones:
Cóncava en los intervalos
[100.194467544685,∞)\left[100.194467544685, \infty\right)
Convexa en los intervalos
(−∞,−99.7456690524054]\left(-\infty, -99.7456690524054\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(xtan⁡6(2)cos⁡2(7x))=⟨−∞,0⟩tan⁡6(2)\lim_{x \to -\infty}\left(x \tan^{6}{\left(2 \right)} \cos^{2}{\left(7 x \right)}\right) = \left\langle -\infty, 0\right\rangle \tan^{6}{\left(2 \right)}
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=⟨−∞,0⟩tan⁡6(2)y = \left\langle -\infty, 0\right\rangle \tan^{6}{\left(2 \right)}
lim⁡x→∞(xtan⁡6(2)cos⁡2(7x))=⟨0,∞⟩tan⁡6(2)\lim_{x \to \infty}\left(x \tan^{6}{\left(2 \right)} \cos^{2}{\left(7 x \right)}\right) = \left\langle 0, \infty\right\rangle \tan^{6}{\left(2 \right)}
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=⟨0,∞⟩tan⁡6(2)y = \left\langle 0, \infty\right\rangle \tan^{6}{\left(2 \right)}
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función (tan(2)^6*x)*cos(7*x)^2, dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(cos⁡2(7x)tan⁡6(2))=⟨0,1⟩tan⁡6(2)\lim_{x \to -\infty}\left(\cos^{2}{\left(7 x \right)} \tan^{6}{\left(2 \right)}\right) = \left\langle 0, 1\right\rangle \tan^{6}{\left(2 \right)}
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=⟨0,1⟩xtan⁡6(2)y = \left\langle 0, 1\right\rangle x \tan^{6}{\left(2 \right)}
lim⁡x→∞(cos⁡2(7x)tan⁡6(2))=⟨0,1⟩tan⁡6(2)\lim_{x \to \infty}\left(\cos^{2}{\left(7 x \right)} \tan^{6}{\left(2 \right)}\right) = \left\langle 0, 1\right\rangle \tan^{6}{\left(2 \right)}
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=⟨0,1⟩xtan⁡6(2)y = \left\langle 0, 1\right\rangle x \tan^{6}{\left(2 \right)}
Paridad e imparidad de la función
Comprobemos si la función es par o impar mediante las relaciones f = f(-x) и f = -f(-x).
Pues, comprobamos:
xtan⁡6(2)cos⁡2(7x)=−xcos⁡2(7x)tan⁡6(2)x \tan^{6}{\left(2 \right)} \cos^{2}{\left(7 x \right)} = - x \cos^{2}{\left(7 x \right)} \tan^{6}{\left(2 \right)}
- No
xtan⁡6(2)cos⁡2(7x)=xcos⁡2(7x)tan⁡6(2)x \tan^{6}{\left(2 \right)} \cos^{2}{\left(7 x \right)} = x \cos^{2}{\left(7 x \right)} \tan^{6}{\left(2 \right)}
- No
es decir, función
no es
par ni impar
Gráfico
Gráfico de la función y = tan(2)^(6)*x*cos(7*x)^2
    © Sr Examen – Калькулятор