Sr Examen
Otras calculadoras
- Gráfico de la función implícita
- Derivadas paso a paso
- Integrales paso a paso
- Gráfico de la función paramétrica
- Gráfico en coordenadas polares
- Superficie especificada paramétricamente
- Superficie dada por la ecuación
- Curva en el espacio especificada paramétricamente
- Superficie de una figura limitada con líneas
- Puntos de cruce de las funciones
-
¿Cómo usar?
- Gráfico de la función y =:
-
x^4-2x^2+10
-
x^3+3*x^2-9*x
-
x^3-6*x+cos(x)+sin(x)
-
-x^3+6x^2
-
Expresiones idénticas
- (dos -x)*(sin(|x|)+cos(|x|))
- (2 menos x) multiplicar por ( seno de ( módulo de x|) más coseno de (|x|))
- (dos menos x) multiplicar por ( seno de ( módulo de x|) más coseno de (|x|))
- (2-x)(sin(|x|)+cos(|x|))
- 2-xsin|x|+cos|x|
-
Expresiones semejantes
- (2+x)*(sin(|x|)+cos(|x|))
- (2-x)*(sin(|x|)-cos(|x|))
-
Expresiones con funciones
- Seno sin
- sin(-x-(pi/3))+1
- sin(x+2)/(x^2-6*x-16)
- sin(x-pi/4)*(-2)
- sin(pi*x)/asin(x)
- sin(x)*e^((1/2)*cot(x)^(2))
- Coseno cos
- cos(sqrt(x^2))
- cos(x):|cos(x)|
- cos(2*x-pi/3)*(-3)
- cos(2π*20.4*t+6.6*sin2πt)
- cos(x-pi)-2
- Módulo |
- |x+5|-|x-4|
- |x|(x+1)-2x
- |2-1/3x|
- |x+1|^1/5
- |(x+2)^2|
Gráfico de la función y = (2-x)*(sin(|x|)+cos(|x|))
Solución
Ha introducido
[src]
f(x) = (2 - x)*(sin(|x|) + cos(|x|))
$$f{\left(x \right)} = \left(2 - x\right) \left(\sin{\left(\left|{x}\right| \right)} + \cos{\left(\left|{x}\right| \right)}\right)$$
f = (2 - x)*(sin(|x|) + cos(|x|))
Gráfico de la función
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:
$$\left(2 - x\right) \left(\sin{\left(\left|{x}\right| \right)} + \cos{\left(\left|{x}\right| \right)}\right) = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución analítica
$$x_{1} = 2$$
Solución numérica
$$x_{1} = 84.037603483527$$
$$x_{2} = -36.9137136796801$$
$$x_{3} = 87.1791961371168$$
$$x_{4} = 49.4800842940392$$
$$x_{5} = -52.621676947629$$
$$x_{6} = -33.7721210260903$$
$$x_{7} = 52.621676947629$$
$$x_{8} = -8.63937979737193$$
$$x_{9} = 90.3207887907066$$
$$x_{10} = 11.7809724509617$$
$$x_{11} = -14.9225651045515$$
$$x_{12} = 93.4623814442964$$
$$x_{13} = -62.0464549083984$$
$$x_{14} = -99.7455667514759$$
$$x_{15} = 74.6128255227576$$
$$x_{16} = 68.329640215578$$
$$x_{17} = -96.6039740978861$$
$$x_{18} = -90.3207887907066$$
$$x_{19} = -24.3473430653209$$
$$x_{20} = -87.1791961371168$$
$$x_{21} = -30.6305283725005$$
$$x_{22} = 36.9137136796801$$
$$x_{23} = 43.1968989868597$$
$$x_{24} = 8.63937979737193$$
$$x_{25} = -80.8960108299372$$
$$x_{26} = -71.4712328691678$$
$$x_{27} = 18.0641577581413$$
$$x_{28} = -46.3384916404494$$
$$x_{29} = -65.1880475619882$$
$$x_{30} = -11.7809724509617$$
$$x_{31} = 58.9048622548086$$
$$x_{32} = 14.9225651045515$$
$$x_{33} = -49.4800842940392$$
$$x_{34} = 46.3384916404494$$
$$x_{35} = -93.4623814442964$$
$$x_{36} = -74.6128255227576$$
$$x_{37} = -2.35619449019234$$
$$x_{38} = -77.7544181763474$$
$$x_{39} = -43.1968989868597$$
$$x_{40} = 77.7544181763474$$
$$x_{41} = -55.7632696012188$$
$$x_{42} = 96.6039740978861$$
$$x_{43} = -40.0553063332699$$
$$x_{44} = 24.3473430653209$$
$$x_{45} = -5.49778714378214$$
$$x_{46} = -27.4889357189107$$
$$x_{47} = -84.037603483527$$
$$x_{48} = 80.8960108299372$$
$$x_{49} = 40.0553063332699$$
$$x_{50} = -58.9048622548086$$
$$x_{51} = 30.6305283725005$$
$$x_{52} = 71.4712328691678$$
$$x_{53} = -68.329640215578$$
$$x_{54} = 65.1880475619882$$
$$x_{55} = 55.7632696012188$$
$$x_{56} = 62.0464549083984$$
$$x_{57} = 27.4889357189107$$
$$x_{58} = 21.2057504117311$$
$$x_{59} = 99.7455667514759$$
$$x_{60} = 5.49778714378214$$
$$x_{61} = 2.35619449019234$$
$$x_{62} = -21.2057504117311$$
$$x_{63} = -18.0641577581413$$
$$x_{64} = 2$$
$$x_{65} = 33.7721210260903$$
o sea hay que resolver la ecuación:
$$\left(2 - x\right) \left(\sin{\left(\left|{x}\right| \right)} + \cos{\left(\left|{x}\right| \right)}\right) = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución analítica
$$x_{1} = 2$$
Solución numérica
$$x_{1} = 84.037603483527$$
$$x_{2} = -36.9137136796801$$
$$x_{3} = 87.1791961371168$$
$$x_{4} = 49.4800842940392$$
$$x_{5} = -52.621676947629$$
$$x_{6} = -33.7721210260903$$
$$x_{7} = 52.621676947629$$
$$x_{8} = -8.63937979737193$$
$$x_{9} = 90.3207887907066$$
$$x_{10} = 11.7809724509617$$
$$x_{11} = -14.9225651045515$$
$$x_{12} = 93.4623814442964$$
$$x_{13} = -62.0464549083984$$
$$x_{14} = -99.7455667514759$$
$$x_{15} = 74.6128255227576$$
$$x_{16} = 68.329640215578$$
$$x_{17} = -96.6039740978861$$
$$x_{18} = -90.3207887907066$$
$$x_{19} = -24.3473430653209$$
$$x_{20} = -87.1791961371168$$
$$x_{21} = -30.6305283725005$$
$$x_{22} = 36.9137136796801$$
$$x_{23} = 43.1968989868597$$
$$x_{24} = 8.63937979737193$$
$$x_{25} = -80.8960108299372$$
$$x_{26} = -71.4712328691678$$
$$x_{27} = 18.0641577581413$$
$$x_{28} = -46.3384916404494$$
$$x_{29} = -65.1880475619882$$
$$x_{30} = -11.7809724509617$$
$$x_{31} = 58.9048622548086$$
$$x_{32} = 14.9225651045515$$
$$x_{33} = -49.4800842940392$$
$$x_{34} = 46.3384916404494$$
$$x_{35} = -93.4623814442964$$
$$x_{36} = -74.6128255227576$$
$$x_{37} = -2.35619449019234$$
$$x_{38} = -77.7544181763474$$
$$x_{39} = -43.1968989868597$$
$$x_{40} = 77.7544181763474$$
$$x_{41} = -55.7632696012188$$
$$x_{42} = 96.6039740978861$$
$$x_{43} = -40.0553063332699$$
$$x_{44} = 24.3473430653209$$
$$x_{45} = -5.49778714378214$$
$$x_{46} = -27.4889357189107$$
$$x_{47} = -84.037603483527$$
$$x_{48} = 80.8960108299372$$
$$x_{49} = 40.0553063332699$$
$$x_{50} = -58.9048622548086$$
$$x_{51} = 30.6305283725005$$
$$x_{52} = 71.4712328691678$$
$$x_{53} = -68.329640215578$$
$$x_{54} = 65.1880475619882$$
$$x_{55} = 55.7632696012188$$
$$x_{56} = 62.0464549083984$$
$$x_{57} = 27.4889357189107$$
$$x_{58} = 21.2057504117311$$
$$x_{59} = 99.7455667514759$$
$$x_{60} = 5.49778714378214$$
$$x_{61} = 2.35619449019234$$
$$x_{62} = -21.2057504117311$$
$$x_{63} = -18.0641577581413$$
$$x_{64} = 2$$
$$x_{65} = 33.7721210260903$$
Extremos de la función
Para hallar los extremos hay que resolver la ecuación
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
$$\frac{d}{d x} f{\left(x \right)} = $$
primera derivada
$$\left(2 - x\right) \left(- \sin{\left(\left|{x}\right| \right)} \operatorname{sign}{\left(x \right)} + \cos{\left(\left|{x}\right| \right)} \operatorname{sign}{\left(x \right)}\right) - \sin{\left(\left|{x}\right| \right)} - \cos{\left(\left|{x}\right| \right)} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 76.1970986495364$$
$$x_{2} = -51.06972152751$$
$$x_{3} = 10.3296572569379$$
$$x_{4} = -41.6490086808161$$
$$x_{5} = 13.4389675712559$$
$$x_{6} = 51.0712563291639$$
$$x_{7} = -104.467348006709$$
$$x_{8} = -19.6810446586041$$
$$x_{9} = 85.620358050592$$
$$x_{10} = -63.6324864134294$$
$$x_{11} = -60.4916593514243$$
$$x_{12} = 16.5619260204649$$
$$x_{13} = -73.0553519079212$$
$$x_{14} = -82.4786439151159$$
$$x_{15} = 98.1851666635936$$
$$x_{16} = 57.3521301149554$$
$$x_{17} = -76.1964094634414$$
$$x_{18} = -91.9022340888408$$
$$x_{19} = 95.0439249692482$$
$$x_{20} = -1.09766089776906$$
$$x_{21} = -85.6198122587075$$
$$x_{22} = -7.1771218627363$$
$$x_{23} = 73.0561016537038$$
$$x_{24} = 2.17903572333602$$
$$x_{25} = -10.2913553205191$$
$$x_{26} = -25.9538973310451$$
$$x_{27} = 29.0966202763459$$
$$x_{28} = -16.547225697059$$
$$x_{29} = 44.7910604279375$$
$$x_{30} = -98.1847516521132$$
$$x_{31} = 47.9310562896495$$
$$x_{32} = 88.7615178008025$$
$$x_{33} = -54.210261743828$$
$$x_{34} = 25.9598516687689$$
$$x_{35} = -22.8168202015565$$
$$x_{36} = -35.3696706368231$$
$$x_{37} = -38.5091907499526$$
$$x_{38} = 38.5118914986711$$
$$x_{39} = -13.4165434160847$$
$$x_{40} = 32.2343875680821$$
$$x_{41} = -88.7610099651303$$
$$x_{42} = 63.6334747609328$$
$$x_{43} = 79.3381440127403$$
$$x_{44} = -95.0434820654718$$
$$x_{45} = -57.3509132742806$$
$$x_{46} = 69.9151597315029$$
$$x_{47} = 101.326430551848$$
$$x_{48} = 22.8245301698031$$
$$x_{49} = 7.25657505489695$$
$$x_{50} = 35.372872846264$$
$$x_{51} = -69.9143410785029$$
$$x_{52} = -29.0918836969137$$
$$x_{53} = -44.7890645756672$$
$$x_{54} = 0.263027254706413$$
$$x_{55} = 4.33207755419064$$
$$x_{56} = -66.7733833731654$$
$$x_{57} = -47.9293136044675$$
$$x_{58} = 66.7742808886442$$
$$x_{59} = 54.211623756215$$
$$x_{60} = -79.3375083346173$$
$$x_{61} = -32.2305300800886$$
$$x_{62} = 19.6914185805939$$
$$x_{63} = 41.6513171583218$$
$$x_{64} = -4.08974865556062$$
$$x_{65} = 91.9027077942952$$
$$x_{66} = 60.4927530512426$$
$$x_{67} = 82.4792320831881$$
Signos de extremos en los puntos:
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:
$$x_{1} = 76.1970986495364$$
$$x_{2} = -41.6490086808161$$
$$x_{3} = 13.4389675712559$$
$$x_{4} = 51.0712563291639$$
$$x_{5} = -104.467348006709$$
$$x_{6} = -60.4916593514243$$
$$x_{7} = -73.0553519079212$$
$$x_{8} = 57.3521301149554$$
$$x_{9} = -91.9022340888408$$
$$x_{10} = 95.0439249692482$$
$$x_{11} = -85.6198122587075$$
$$x_{12} = 2.17903572333602$$
$$x_{13} = -10.2913553205191$$
$$x_{14} = -16.547225697059$$
$$x_{15} = 44.7910604279375$$
$$x_{16} = -98.1847516521132$$
$$x_{17} = 88.7615178008025$$
$$x_{18} = -54.210261743828$$
$$x_{19} = 25.9598516687689$$
$$x_{20} = -22.8168202015565$$
$$x_{21} = -35.3696706368231$$
$$x_{22} = 38.5118914986711$$
$$x_{23} = 32.2343875680821$$
$$x_{24} = 63.6334747609328$$
$$x_{25} = 69.9151597315029$$
$$x_{26} = 101.326430551848$$
$$x_{27} = 7.25657505489695$$
$$x_{28} = -29.0918836969137$$
$$x_{29} = -66.7733833731654$$
$$x_{30} = -47.9293136044675$$
$$x_{31} = -79.3375083346173$$
$$x_{32} = 19.6914185805939$$
$$x_{33} = -4.08974865556062$$
$$x_{34} = 82.4792320831881$$
Puntos máximos de la función:
$$x_{34} = -51.06972152751$$
$$x_{34} = 10.3296572569379$$
$$x_{34} = -19.6810446586041$$
$$x_{34} = 85.620358050592$$
$$x_{34} = -63.6324864134294$$
$$x_{34} = 16.5619260204649$$
$$x_{34} = -82.4786439151159$$
$$x_{34} = 98.1851666635936$$
$$x_{34} = -76.1964094634414$$
$$x_{34} = -1.09766089776906$$
$$x_{34} = -7.1771218627363$$
$$x_{34} = 73.0561016537038$$
$$x_{34} = -25.9538973310451$$
$$x_{34} = 29.0966202763459$$
$$x_{34} = 47.9310562896495$$
$$x_{34} = -38.5091907499526$$
$$x_{34} = -13.4165434160847$$
$$x_{34} = -88.7610099651303$$
$$x_{34} = 79.3381440127403$$
$$x_{34} = -95.0434820654718$$
$$x_{34} = -57.3509132742806$$
$$x_{34} = 22.8245301698031$$
$$x_{34} = 35.372872846264$$
$$x_{34} = -69.9143410785029$$
$$x_{34} = -44.7890645756672$$
$$x_{34} = 0.263027254706413$$
$$x_{34} = 4.33207755419064$$
$$x_{34} = 66.7742808886442$$
$$x_{34} = 54.211623756215$$
$$x_{34} = -32.2305300800886$$
$$x_{34} = 41.6513171583218$$
$$x_{34} = 91.9027077942952$$
$$x_{34} = 60.4927530512426$$
Decrece en los intervalos
$$\left[101.326430551848, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -104.467348006709\right]$$
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
$$\frac{d}{d x} f{\left(x \right)} = $$
primera derivada
$$\left(2 - x\right) \left(- \sin{\left(\left|{x}\right| \right)} \operatorname{sign}{\left(x \right)} + \cos{\left(\left|{x}\right| \right)} \operatorname{sign}{\left(x \right)}\right) - \sin{\left(\left|{x}\right| \right)} - \cos{\left(\left|{x}\right| \right)} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 76.1970986495364$$
$$x_{2} = -51.06972152751$$
$$x_{3} = 10.3296572569379$$
$$x_{4} = -41.6490086808161$$
$$x_{5} = 13.4389675712559$$
$$x_{6} = 51.0712563291639$$
$$x_{7} = -104.467348006709$$
$$x_{8} = -19.6810446586041$$
$$x_{9} = 85.620358050592$$
$$x_{10} = -63.6324864134294$$
$$x_{11} = -60.4916593514243$$
$$x_{12} = 16.5619260204649$$
$$x_{13} = -73.0553519079212$$
$$x_{14} = -82.4786439151159$$
$$x_{15} = 98.1851666635936$$
$$x_{16} = 57.3521301149554$$
$$x_{17} = -76.1964094634414$$
$$x_{18} = -91.9022340888408$$
$$x_{19} = 95.0439249692482$$
$$x_{20} = -1.09766089776906$$
$$x_{21} = -85.6198122587075$$
$$x_{22} = -7.1771218627363$$
$$x_{23} = 73.0561016537038$$
$$x_{24} = 2.17903572333602$$
$$x_{25} = -10.2913553205191$$
$$x_{26} = -25.9538973310451$$
$$x_{27} = 29.0966202763459$$
$$x_{28} = -16.547225697059$$
$$x_{29} = 44.7910604279375$$
$$x_{30} = -98.1847516521132$$
$$x_{31} = 47.9310562896495$$
$$x_{32} = 88.7615178008025$$
$$x_{33} = -54.210261743828$$
$$x_{34} = 25.9598516687689$$
$$x_{35} = -22.8168202015565$$
$$x_{36} = -35.3696706368231$$
$$x_{37} = -38.5091907499526$$
$$x_{38} = 38.5118914986711$$
$$x_{39} = -13.4165434160847$$
$$x_{40} = 32.2343875680821$$
$$x_{41} = -88.7610099651303$$
$$x_{42} = 63.6334747609328$$
$$x_{43} = 79.3381440127403$$
$$x_{44} = -95.0434820654718$$
$$x_{45} = -57.3509132742806$$
$$x_{46} = 69.9151597315029$$
$$x_{47} = 101.326430551848$$
$$x_{48} = 22.8245301698031$$
$$x_{49} = 7.25657505489695$$
$$x_{50} = 35.372872846264$$
$$x_{51} = -69.9143410785029$$
$$x_{52} = -29.0918836969137$$
$$x_{53} = -44.7890645756672$$
$$x_{54} = 0.263027254706413$$
$$x_{55} = 4.33207755419064$$
$$x_{56} = -66.7733833731654$$
$$x_{57} = -47.9293136044675$$
$$x_{58} = 66.7742808886442$$
$$x_{59} = 54.211623756215$$
$$x_{60} = -79.3375083346173$$
$$x_{61} = -32.2305300800886$$
$$x_{62} = 19.6914185805939$$
$$x_{63} = 41.6513171583218$$
$$x_{64} = -4.08974865556062$$
$$x_{65} = 91.9027077942952$$
$$x_{66} = 60.4927530512426$$
$$x_{67} = 82.4792320831881$$
Signos de extremos en los puntos:
(76.19709864953641, -104.921014383413)
(-51.06972152750996, 75.0385993731921)
(10.329657256937894, 11.695930741592)
(-41.64900868081614, -61.7128265988845)
(13.438967571255922, -16.1156795372477)
(51.07125632916393, -69.3828309142045)
(-104.46734800670926, -150.560926403858)
(-19.681044658604105, 30.6290652918276)
(85.62035805059199, 118.248589196674)
(-63.63248641342937, 92.8075805621684)
(-60.49165935142426, -88.3652391441028)
(16.561926020464906, 20.545285744725)
(-73.05535190792122, -106.134876713605)
(-82.47864391511587, 119.462474592143)
(98.1851666635936, 136.019016274793)
(57.352130114955415, -78.2669615424326)
(-76.19640946344138, 110.577381199668)
(-91.90223408884084, -132.790283381517)
(95.04392496924822, -131.576381536968)
(-1.0976608977690603, 4.16890458034267)
(-85.61981225870753, -123.90505744714)
(-7.177121862736295, 12.9020386046531)
(73.05610165370385, 100.478552738806)
(2.17903572333602, -0.0446214030337907)
(-10.291355320519108, -17.325356632034)
(-25.95389733104508, 39.5075095160384)
(29.09662027634593, 38.2943387597944)
(-16.547225697058977, -26.1916963792683)
(44.79106042793752, -60.4991801329014)
(-98.18475165211325, -141.675577028768)
(47.93105628964952, 64.9409332496534)
(88.76151780080245, -122.691165973158)
(-54.21026174382804, -79.4807378137109)
(25.959851668768867, -33.8548735308394)
(-22.81682020155651, -35.0678253101469)
(-35.36967063682312, -52.8297832490745)
(-38.509190749952644, 57.2711994676464)
(38.511891498671076, -51.6162565548779)
(-13.416543416084677, 21.7565622647035)
(32.23438756808213, -42.7345126185387)
(-88.76100996513028, 128.347661071567)
(63.6334747609328, -87.1514253961028)
(79.3381440127403, 109.363510244489)
(-95.04348206547185, 137.232922562819)
(-57.35091327428056, 83.92295502778)
(69.91515973150292, -96.0361300564761)
(101.32643055184802, -140.461666710328)
(22.824530169803058, 29.4164361347947)
(7.256575054896953, -7.30294567629717)
(35.37287284626396, 47.1751955814942)
(-69.91434107850294, 101.692405282587)
(-29.091883696913687, -43.9478387453793)
(-44.78906457566725, 66.1546222185845)
(0.2630272547064127, 2.12885495459675)
(4.33207755419064, 3.03113817900633)
(-66.7733833731654, -97.2499714341767)
(-47.929313604467495, -70.5965545616187)
(66.77428088864424, 91.5937520022301)
(54.211623756215026, 73.8248470632575)
(-79.33750833461727, -115.019914912285)
(-32.230530080088585, 48.3886359029811)
(19.691418580593886, -24.9795707027244)
(41.65131715832176, 56.0576058715679)
(-4.089748655560621, -8.49838757857203)
(91.90270779429521, 127.133764141988)
(60.49275305124256, 82.7091585219687)
(82.4792320831881, -113.806036316801)
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:
$$x_{1} = 76.1970986495364$$
$$x_{2} = -41.6490086808161$$
$$x_{3} = 13.4389675712559$$
$$x_{4} = 51.0712563291639$$
$$x_{5} = -104.467348006709$$
$$x_{6} = -60.4916593514243$$
$$x_{7} = -73.0553519079212$$
$$x_{8} = 57.3521301149554$$
$$x_{9} = -91.9022340888408$$
$$x_{10} = 95.0439249692482$$
$$x_{11} = -85.6198122587075$$
$$x_{12} = 2.17903572333602$$
$$x_{13} = -10.2913553205191$$
$$x_{14} = -16.547225697059$$
$$x_{15} = 44.7910604279375$$
$$x_{16} = -98.1847516521132$$
$$x_{17} = 88.7615178008025$$
$$x_{18} = -54.210261743828$$
$$x_{19} = 25.9598516687689$$
$$x_{20} = -22.8168202015565$$
$$x_{21} = -35.3696706368231$$
$$x_{22} = 38.5118914986711$$
$$x_{23} = 32.2343875680821$$
$$x_{24} = 63.6334747609328$$
$$x_{25} = 69.9151597315029$$
$$x_{26} = 101.326430551848$$
$$x_{27} = 7.25657505489695$$
$$x_{28} = -29.0918836969137$$
$$x_{29} = -66.7733833731654$$
$$x_{30} = -47.9293136044675$$
$$x_{31} = -79.3375083346173$$
$$x_{32} = 19.6914185805939$$
$$x_{33} = -4.08974865556062$$
$$x_{34} = 82.4792320831881$$
Puntos máximos de la función:
$$x_{34} = -51.06972152751$$
$$x_{34} = 10.3296572569379$$
$$x_{34} = -19.6810446586041$$
$$x_{34} = 85.620358050592$$
$$x_{34} = -63.6324864134294$$
$$x_{34} = 16.5619260204649$$
$$x_{34} = -82.4786439151159$$
$$x_{34} = 98.1851666635936$$
$$x_{34} = -76.1964094634414$$
$$x_{34} = -1.09766089776906$$
$$x_{34} = -7.1771218627363$$
$$x_{34} = 73.0561016537038$$
$$x_{34} = -25.9538973310451$$
$$x_{34} = 29.0966202763459$$
$$x_{34} = 47.9310562896495$$
$$x_{34} = -38.5091907499526$$
$$x_{34} = -13.4165434160847$$
$$x_{34} = -88.7610099651303$$
$$x_{34} = 79.3381440127403$$
$$x_{34} = -95.0434820654718$$
$$x_{34} = -57.3509132742806$$
$$x_{34} = 22.8245301698031$$
$$x_{34} = 35.372872846264$$
$$x_{34} = -69.9143410785029$$
$$x_{34} = -44.7890645756672$$
$$x_{34} = 0.263027254706413$$
$$x_{34} = 4.33207755419064$$
$$x_{34} = 66.7742808886442$$
$$x_{34} = 54.211623756215$$
$$x_{34} = -32.2305300800886$$
$$x_{34} = 41.6513171583218$$
$$x_{34} = 91.9027077942952$$
$$x_{34} = 60.4927530512426$$
Decrece en los intervalos
$$\left[101.326430551848, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -104.467348006709\right]$$
Puntos de flexiones
Hallemos los puntos de flexiones, para eso hay que resolver la ecuación
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(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:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$
segunda derivada
$$\left(x - 2\right) \left(2 \sin{\left(\left|{x}\right| \right)} \delta\left(x\right) + \sin{\left(\left|{x}\right| \right)} \operatorname{sign}^{2}{\left(x \right)} - 2 \cos{\left(\left|{x}\right| \right)} \delta\left(x\right) + \cos{\left(\left|{x}\right| \right)} \operatorname{sign}^{2}{\left(x \right)}\right) + 2 \sin{\left(\left|{x}\right| \right)} \operatorname{sign}{\left(x \right)} - 2 \cos{\left(\left|{x}\right| \right)} \operatorname{sign}{\left(x \right)} = 0$$
Resolvermos esta ecuación
Soluciones no halladas,
tal vez la función no tenga flexiones
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(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:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$
segunda derivada
$$\left(x - 2\right) \left(2 \sin{\left(\left|{x}\right| \right)} \delta\left(x\right) + \sin{\left(\left|{x}\right| \right)} \operatorname{sign}^{2}{\left(x \right)} - 2 \cos{\left(\left|{x}\right| \right)} \delta\left(x\right) + \cos{\left(\left|{x}\right| \right)} \operatorname{sign}^{2}{\left(x \right)}\right) + 2 \sin{\left(\left|{x}\right| \right)} \operatorname{sign}{\left(x \right)} - 2 \cos{\left(\left|{x}\right| \right)} \operatorname{sign}{\left(x \right)} = 0$$
Resolvermos esta ecuación
Soluciones no halladas,
tal vez la función no tenga flexiones
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
$$\lim_{x \to -\infty}\left(\left(2 - x\right) \left(\sin{\left(\left|{x}\right| \right)} + \cos{\left(\left|{x}\right| \right)}\right)\right) = \left\langle -\infty, \infty\right\rangle$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \left\langle -\infty, \infty\right\rangle$$
$$\lim_{x \to \infty}\left(\left(2 - x\right) \left(\sin{\left(\left|{x}\right| \right)} + \cos{\left(\left|{x}\right| \right)}\right)\right) = \left\langle -\infty, \infty\right\rangle$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \left\langle -\infty, \infty\right\rangle$$
$$\lim_{x \to -\infty}\left(\left(2 - x\right) \left(\sin{\left(\left|{x}\right| \right)} + \cos{\left(\left|{x}\right| \right)}\right)\right) = \left\langle -\infty, \infty\right\rangle$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \left\langle -\infty, \infty\right\rangle$$
$$\lim_{x \to \infty}\left(\left(2 - x\right) \left(\sin{\left(\left|{x}\right| \right)} + \cos{\left(\left|{x}\right| \right)}\right)\right) = \left\langle -\infty, \infty\right\rangle$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \left\langle -\infty, \infty\right\rangle$$
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función (2 - x)*(sin(|x|) + cos(|x|)), dividida por x con x->+oo y x ->-oo
$$\lim_{x \to -\infty}\left(\frac{\left(2 - x\right) \left(\sin{\left(\left|{x}\right| \right)} + \cos{\left(\left|{x}\right| \right)}\right)}{x}\right) = \left\langle -2, 2\right\rangle$$
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
$$y = \left\langle -2, 2\right\rangle x$$
$$\lim_{x \to \infty}\left(\frac{\left(2 - x\right) \left(\sin{\left(\left|{x}\right| \right)} + \cos{\left(\left|{x}\right| \right)}\right)}{x}\right) = \left\langle -2, 2\right\rangle$$
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
$$y = \left\langle -2, 2\right\rangle x$$
$$\lim_{x \to -\infty}\left(\frac{\left(2 - x\right) \left(\sin{\left(\left|{x}\right| \right)} + \cos{\left(\left|{x}\right| \right)}\right)}{x}\right) = \left\langle -2, 2\right\rangle$$
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
$$y = \left\langle -2, 2\right\rangle x$$
$$\lim_{x \to \infty}\left(\frac{\left(2 - x\right) \left(\sin{\left(\left|{x}\right| \right)} + \cos{\left(\left|{x}\right| \right)}\right)}{x}\right) = \left\langle -2, 2\right\rangle$$
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
$$y = \left\langle -2, 2\right\rangle x$$
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:
$$\left(2 - x\right) \left(\sin{\left(\left|{x}\right| \right)} + \cos{\left(\left|{x}\right| \right)}\right) = \left(x + 2\right) \left(\sin{\left(\left|{x}\right| \right)} + \cos{\left(\left|{x}\right| \right)}\right)$$
- No
$$\left(2 - x\right) \left(\sin{\left(\left|{x}\right| \right)} + \cos{\left(\left|{x}\right| \right)}\right) = - \left(x + 2\right) \left(\sin{\left(\left|{x}\right| \right)} + \cos{\left(\left|{x}\right| \right)}\right)$$
- No
es decir, función
no es
par ni impar
Pues, comprobamos:
$$\left(2 - x\right) \left(\sin{\left(\left|{x}\right| \right)} + \cos{\left(\left|{x}\right| \right)}\right) = \left(x + 2\right) \left(\sin{\left(\left|{x}\right| \right)} + \cos{\left(\left|{x}\right| \right)}\right)$$
- No
$$\left(2 - x\right) \left(\sin{\left(\left|{x}\right| \right)} + \cos{\left(\left|{x}\right| \right)}\right) = - \left(x + 2\right) \left(\sin{\left(\left|{x}\right| \right)} + \cos{\left(\left|{x}\right| \right)}\right)$$
- No
es decir, función
no es
par ni impar