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Trazado el gráfico de la función/ -1+(-1-x)*cos(x*sqrt(2)/2)+(-1-x)*sin(x*sqrt(2)/2)

Gráfico de la función y = -1+(-1-x)*cos(x*sqrt(2)/2)+(-1-x)*sin(x*sqrt(2)/2)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
                        /    ___\               /    ___\
                        |x*\/ 2 |               |x*\/ 2 |
f(x) = -1 + (-1 - x)*cos|-------| + (-1 - x)*sin|-------|
                        \   2   /               \   2   /
f(x)=(−x−1)sin⁡(2x2)+((−x−1)cos⁡(2x2)−1)f{\left(x \right)} = \left(- x - 1\right) \sin{\left(\frac{\sqrt{2} x}{2} \right)} + \left(\left(- x - 1\right) \cos{\left(\frac{\sqrt{2} x}{2} \right)} - 1\right) 
f = (-x - 1)*sin((sqrt(2)*x)/2) + (-x - 1)*cos((sqrt(2)*x)/2) - 1
Gráfico de la función
02468-8-6-4-2-1010-2525
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:
(−x−1)sin⁡(2x2)+((−x−1)cos⁡(2x2)−1)=0\left(- x - 1\right) \sin{\left(\frac{\sqrt{2} x}{2} \right)} + \left(\left(- x - 1\right) \cos{\left(\frac{\sqrt{2} x}{2} \right)} - 1\right) = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=78.8486482950879x_{1} = 78.8486482950879
x2=87.7356684839146x_{2} = 87.7356684839146
x3=96.6224602710347x_{3} = 96.6224602710347
x4=−98.8439249264527x_{4} = -98.8439249264527
x5=−36.6257127826445x_{5} = -36.6257127826445
x6=21.1488506987593x_{6} = 21.1488506987593
x7=34.4040955727992x_{7} = 34.4040955727992
x8=56.6640997085722x_{8} = 56.6640997085722
x9=−76.652949131055x_{9} = -76.652949131055
x10=−72.1827991763375x_{10} = -72.1827991763375
x11=−81.0701244063939x_{11} = -81.0701244063939
x12=−18.8261403727126x_{12} = -18.8261403727126
x13=30.0216981262351x_{13} = 30.0216981262351
x14=−54.4065911647164x_{14} = -54.4065911647164
x15=−32.2429112952846x_{15} = -32.2429112952846
x16=65.54755046973x_{16} = 65.54755046973
x17=61.0735301248675x_{17} = 61.0735301248675
x18=−67.7689421101633x_{18} = -67.7689421101633
x19=−9.88380300947023x_{19} = -9.88380300947023
x20=83.315915386568x_{20} = 83.315915386568
x21=38.9002894957406x_{21} = 38.9002894957406
x22=−50.0028407427305x_{22} = -50.0028407427305
x23=12.2931900885414x_{23} = 12.2931900885414
x24=−89.9571380104765x_{24} = -89.9571380104765
x25=−85.5373257918033x_{25} = -85.5373257918033
x26=101.085382643154x_{26} = 101.085382643154
x27=−23.3698459078779x_{27} = -23.3698459078779
x28=92.2005506200682x_{28} = 92.2005506200682
x29=−14.513403960098x_{29} = -14.513403960098
x30=16.6039904294345x_{30} = 16.6039904294345
x31=52.1850717008618x_{31} = 52.1850717008618
x32=7.65943544932799x_{32} = 7.65943544932799
x33=69.9613138572449x_{33} = 69.9613138572449
x34=−27.7306036954298x_{34} = -27.7306036954298
x35=43.295532047774x_{35} = 43.295532047774
x36=−41.1215927032987x_{36} = -41.1215927032987
x37=74.4315464611969x_{37} = 74.4315464611969
x38=−58.8854748512754x_{38} = -58.8854748512754
x39=−45.5170858861585x_{39} = -45.5170858861585
x40=25.508849167392x_{40} = 25.508849167392
x41=−5.76427742810406x_{41} = -5.76427742810406
x42=−94.4219666586963x_{42} = -94.4219666586963
x43=−63.2950288787638x_{43} = -63.2950288787638
x44=47.7814918811987x_{44} = 47.7814918811987
x45=3.55270468296405x_{45} = 3.55270468296405
x46=−209.931005106154x_{46} = -209.931005106154
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 -1 + (-1 - x)*cos((x*sqrt(2))/2) + (-1 - x)*sin((x*sqrt(2))/2).
(−1+(−1−0)cos⁡(022))+(−1−0)sin⁡(022)\left(-1 + \left(-1 - 0\right) \cos{\left(\frac{0 \sqrt{2}}{2} \right)}\right) + \left(-1 - 0\right) \sin{\left(\frac{0 \sqrt{2}}{2} \right)}
Resultado:
f(0)=−2f{\left(0 \right)} = -2
Punto:
(0, -2)
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
−2(−x−1)sin⁡(2x2)2+2(−x−1)cos⁡(2x2)2−sin⁡(2x2)−cos⁡(2x2)=0- \frac{\sqrt{2} \left(- x - 1\right) \sin{\left(\frac{\sqrt{2} x}{2} \right)}}{2} + \frac{\sqrt{2} \left(- x - 1\right) \cos{\left(\frac{\sqrt{2} x}{2} \right)}}{2} - \sin{\left(\frac{\sqrt{2} x}{2} \right)} - \cos{\left(\frac{\sqrt{2} x}{2} \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−56.6826675610891x_{1} = -56.6826675610891
x2=−25.6276971876651x_{2} = -25.6276971876651
x3=−30.0582328781461x_{3} = -30.0582328781461
x4=63.3421606824646x_{4} = 63.3421606824646
x5=50.0216220875817x_{5} = 50.0216220875817
x6=1.77687936809853x_{6} = 1.77687936809853
x7=−38.9279328760707x_{7} = -38.9279328760707
x8=54.4613693161347x_{8} = 54.4613693161347
x9=10.1745187671212x_{9} = 10.1745187671212
x10=−3.96210099634574x_{10} = -3.96210099634574
x11=89.9903580789576x_{11} = 89.9903580789576
x12=−8.05483051308111x_{12} = -8.05483051308111
x13=32.2709775887511x_{13} = 32.2709775887511
x14=98.8741692336653x_{14} = 98.8741692336653
x15=45.5824715372825x_{15} = 45.5824715372825
x16=−78.8868476073282x_{16} = -78.8868476073282
x17=58.9015808298421x_{17} = 58.9015808298421
x18=−70.0043858839905x_{18} = -70.0043858839905
x19=−16.7871590134849x_{19} = -16.7871590134849
x20=5.84186222701659x_{20} = 5.84186222701659
x21=23.4069876500919x_{21} = 23.4069876500919
x22=27.8373174223413x_{22} = 27.8373174223413
x23=67.7830376469223x_{23} = 67.7830376469223
x24=−12.3925873529074x_{24} = -12.3925873529074
x25=−87.7699854329339x_{25} = -87.7699854329339
x26=−92.211746210428x_{26} = -92.211746210428
x27=−52.242894420254x_{27} = -52.242894420254
x28=41.144105598611x_{28} = 41.144105598611
x29=−1.05537450400253x_{29} = -1.05537450400253
x30=−83.3283456710998x_{30} = -83.3283456710998
x31=36.7068002210725x_{31} = 36.7068002210725
x32=72.224157740075x_{32} = 72.224157740075
x33=81.1069696811089x_{33} = 81.1069696811089
x34=14.5674907317375x_{34} = 14.5674907317375
x35=−65.5634956420564x_{35} = -65.5634956420564
x36=−43.3652995706866x_{36} = -43.3652995706866
x37=94.4322181849273x_{37} = 94.4322181849273
x38=85.5486029062939x_{38} = 85.5486029062939
x39=−61.1228994620739x_{39} = -61.1228994620739
x40=18.9821750786416x_{40} = 18.9821750786416
x41=−47.8037102427204x_{41} = -47.8037102427204
x42=−34.4920230298981x_{42} = -34.4920230298981
x43=76.6654793043163x_{43} = 76.6654793043163
x44=−101.095566418709x_{44} = -101.095566418709
x45=−74.4455169192843x_{45} = -74.4455169192843
x46=−96.6536111584108x_{46} = -96.6536111584108
x47=−21.2025302264653x_{47} = -21.2025302264653
Signos de extremos en los puntos:
                                               /                   ___\                       /                   ___\ 
(-56.682667561089104, -1 + 55.6826675610891*cos\28.3413337805446*\/ 2 / - 55.6826675610891*sin\28.3413337805446*\/ 2 /)

                                               /                   ___\                       /                   ___\ 
(-25.627697187665067, -1 + 24.6276971876651*cos\12.8138485938325*\/ 2 / - 24.6276971876651*sin\12.8138485938325*\/ 2 /)

                                              /                  ___\                       /                  ___\ 
(-30.05823287814606, -1 + 29.0582328781461*cos\15.029116439073*\/ 2 / - 29.0582328781461*sin\15.029116439073*\/ 2 /)

                                            /                   ___\                       /                   ___\ 
(63.3421606824646, -1 - 64.3421606824646*cos\31.6710803412323*\/ 2 / - 64.3421606824646*sin\31.6710803412323*\/ 2 /)

                                            /                   ___\                       /                   ___\ 
(50.0216220875817, -1 - 51.0216220875817*cos\25.0108110437908*\/ 2 / - 51.0216220875817*sin\25.0108110437908*\/ 2 /)

                                              /                    ___\                       /                    ___\ 
(1.7768793680985289, -1 - 2.77687936809853*cos\0.888439684049264*\/ 2 / - 2.77687936809853*sin\0.888439684049264*\/ 2 /)

                                               /                   ___\                       /                   ___\ 
(-38.927932876070706, -1 + 37.9279328760707*cos\19.4639664380354*\/ 2 / - 37.9279328760707*sin\19.4639664380354*\/ 2 /)

                                             /                   ___\                       /                   ___\ 
(54.46136931613474, -1 - 55.4613693161347*cos\27.2306846580674*\/ 2 / - 55.4613693161347*sin\27.2306846580674*\/ 2 /)

                                              /                   ___\                       /                   ___\ 
(10.174518767121183, -1 - 11.1745187671212*cos\5.08725938356059*\/ 2 / - 11.1745187671212*sin\5.08725938356059*\/ 2 /)

                                              /                   ___\                       /                   ___\ 
(-3.962100996345738, -1 + 2.96210099634574*cos\1.98105049817287*\/ 2 / - 2.96210099634574*sin\1.98105049817287*\/ 2 /)

                                             /                   ___\                       /                   ___\ 
(89.99035807895756, -1 - 90.9903580789576*cos\44.9951790394788*\/ 2 / - 90.9903580789576*sin\44.9951790394788*\/ 2 /)

                                              /                   ___\                       /                   ___\ 
(-8.054830513081113, -1 + 7.05483051308111*cos\4.02741525654056*\/ 2 / - 7.05483051308111*sin\4.02741525654056*\/ 2 /)

                                              /                   ___\                       /                   ___\ 
(32.270977588751094, -1 - 33.2709775887511*cos\16.1354887943755*\/ 2 / - 33.2709775887511*sin\16.1354887943755*\/ 2 /)

                                             /                   ___\                       /                   ___\ 
(98.87416923366531, -1 - 99.8741692336653*cos\49.4370846168327*\/ 2 / - 99.8741692336653*sin\49.4370846168327*\/ 2 /)

                                              /                   ___\                       /                   ___\ 
(45.582471537282466, -1 - 46.5824715372825*cos\22.7912357686412*\/ 2 / - 46.5824715372825*sin\22.7912357686412*\/ 2 /)

                                             /                   ___\                       /                   ___\ 
(-78.8868476073282, -1 + 77.8868476073282*cos\39.4434238036641*\/ 2 / - 77.8868476073282*sin\39.4434238036641*\/ 2 /)

                                              /                  ___\                       /                  ___\ 
(58.901580829842096, -1 - 59.9015808298421*cos\29.450790414921*\/ 2 / - 59.9015808298421*sin\29.450790414921*\/ 2 /)

                                              /                   ___\                       /                   ___\ 
(-70.00438588399047, -1 + 69.0043858839905*cos\35.0021929419952*\/ 2 / - 69.0043858839905*sin\35.0021929419952*\/ 2 /)

                                               /                   ___\                       /                   ___\ 
(-16.787159013484853, -1 + 15.7871590134849*cos\8.39357950674243*\/ 2 / - 15.7871590134849*sin\8.39357950674243*\/ 2 /)

                                             /                   ___\                       /                   ___\ 
(5.841862227016587, -1 - 6.84186222701659*cos\2.92093111350829*\/ 2 / - 6.84186222701659*sin\2.92093111350829*\/ 2 /)

                                             /                  ___\                       /                  ___\ 
(23.40698765009192, -1 - 24.4069876500919*cos\11.703493825046*\/ 2 / - 24.4069876500919*sin\11.703493825046*\/ 2 /)

                                              /                   ___\                       /                   ___\ 
(27.837317422341297, -1 - 28.8373174223413*cos\13.9186587111706*\/ 2 / - 28.8373174223413*sin\13.9186587111706*\/ 2 /)

                                             /                   ___\                       /                   ___\ 
(67.78303764692231, -1 - 68.7830376469223*cos\33.8915188234612*\/ 2 / - 68.7830376469223*sin\33.8915188234612*\/ 2 /)

                                               /                   ___\                       /                   ___\ 
(-12.392587352907352, -1 + 11.3925873529074*cos\6.19629367645368*\/ 2 / - 11.3925873529074*sin\6.19629367645368*\/ 2 /)

                                              /                  ___\                       /                  ___\ 
(-87.76998543293394, -1 + 86.7699854329339*cos\43.884992716467*\/ 2 / - 86.7699854329339*sin\43.884992716467*\/ 2 /)

                                             /                  ___\                      /                  ___\ 
(-92.21174621042796, -1 + 91.211746210428*cos\46.105873105214*\/ 2 / - 91.211746210428*sin\46.105873105214*\/ 2 /)

                                              /                  ___\                      /                  ___\ 
(-52.242894420254046, -1 + 51.242894420254*cos\26.121447210127*\/ 2 / - 51.242894420254*sin\26.121447210127*\/ 2 /)

                                             /                   ___\                      /                   ___\ 
(41.144105598610956, -1 - 42.144105598611*cos\20.5720527993055*\/ 2 / - 42.144105598611*sin\20.5720527993055*\/ 2 /)

                                                 /                    ___\                         /                    ___\ 
(-1.0553745040025266, -1 + 0.0553745040025266*cos\0.527687252001263*\/ 2 / - 0.0553745040025266*sin\0.527687252001263*\/ 2 /)

                                              /                   ___\                       /                   ___\ 
(-83.32834567109983, -1 + 82.3283456710998*cos\41.6641728355499*\/ 2 / - 82.3283456710998*sin\41.6641728355499*\/ 2 /)

                                              /                   ___\                       /                   ___\ 
(36.706800221072506, -1 - 37.7068002210725*cos\18.3534001105363*\/ 2 / - 37.7068002210725*sin\18.3534001105363*\/ 2 /)

                                            /                   ___\                      /                   ___\ 
(72.22415774007503, -1 - 73.224157740075*cos\36.1120788700375*\/ 2 / - 73.224157740075*sin\36.1120788700375*\/ 2 /)

                                            /                   ___\                       /                   ___\ 
(81.1069696811089, -1 - 82.1069696811089*cos\40.5534848405544*\/ 2 / - 82.1069696811089*sin\40.5534848405544*\/ 2 /)

                                              /                   ___\                       /                   ___\ 
(14.567490731737491, -1 - 15.5674907317375*cos\7.28374536586875*\/ 2 / - 15.5674907317375*sin\7.28374536586875*\/ 2 /)

                                              /                   ___\                       /                   ___\ 
(-65.56349564205641, -1 + 64.5634956420564*cos\32.7817478210282*\/ 2 / - 64.5634956420564*sin\32.7817478210282*\/ 2 /)

                                              /                   ___\                       /                   ___\ 
(-43.36529957068655, -1 + 42.3652995706866*cos\21.6826497853433*\/ 2 / - 42.3652995706866*sin\21.6826497853433*\/ 2 /)

                                             /                   ___\                       /                   ___\ 
(94.43221818492732, -1 - 95.4322181849273*cos\47.2161090924637*\/ 2 / - 95.4322181849273*sin\47.2161090924637*\/ 2 /)

                                             /                  ___\                       /                  ___\ 
(85.54860290629391, -1 - 86.5486029062939*cos\42.774301453147*\/ 2 / - 86.5486029062939*sin\42.774301453147*\/ 2 /)

                                              /                  ___\                       /                  ___\ 
(-61.12289946207391, -1 + 60.1228994620739*cos\30.561449731037*\/ 2 / - 60.1228994620739*sin\30.561449731037*\/ 2 /)

                                             /                   ___\                       /                   ___\ 
(18.98217507864162, -1 - 19.9821750786416*cos\9.49108753932081*\/ 2 / - 19.9821750786416*sin\9.49108753932081*\/ 2 /)

                                              /                   ___\                       /                   ___\ 
(-47.80371024272038, -1 + 46.8037102427204*cos\23.9018551213602*\/ 2 / - 46.8037102427204*sin\23.9018551213602*\/ 2 /)

                                               /                  ___\                       /                  ___\ 
(-34.492023029898064, -1 + 33.4920230298981*cos\17.246011514949*\/ 2 / - 33.4920230298981*sin\17.246011514949*\/ 2 /)

                                             /                   ___\                       /                   ___\ 
(76.66547930431632, -1 - 77.6654793043163*cos\38.3327396521582*\/ 2 / - 77.6654793043163*sin\38.3327396521582*\/ 2 /)

                                               /                   ___\                       /                   ___\ 
(-101.09556641870877, -1 + 100.095566418709*cos\50.5477832093544*\/ 2 / - 100.095566418709*sin\50.5477832093544*\/ 2 /)

                                              /                   ___\                       /                   ___\ 
(-74.44551691928426, -1 + 73.4455169192843*cos\37.2227584596421*\/ 2 / - 73.4455169192843*sin\37.2227584596421*\/ 2 /)

                                              /                   ___\                       /                   ___\ 
(-96.65361115841083, -1 + 95.6536111584108*cos\48.3268055792054*\/ 2 / - 95.6536111584108*sin\48.3268055792054*\/ 2 /)

                                               /                   ___\                       /                   ___\ 
(-21.202530226465328, -1 + 20.2025302264653*cos\10.6012651132327*\/ 2 / - 20.2025302264653*sin\10.6012651132327*\/ 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=−56.6826675610891x_{1} = -56.6826675610891
x2=−30.0582328781461x_{2} = -30.0582328781461
x3=63.3421606824646x_{3} = 63.3421606824646
x4=1.77687936809853x_{4} = 1.77687936809853
x5=−38.9279328760707x_{5} = -38.9279328760707
x6=54.4613693161347x_{6} = 54.4613693161347
x7=10.1745187671212x_{7} = 10.1745187671212
x8=−3.96210099634574x_{8} = -3.96210099634574
x9=89.9903580789576x_{9} = 89.9903580789576
x10=98.8741692336653x_{10} = 98.8741692336653
x11=45.5824715372825x_{11} = 45.5824715372825
x12=27.8373174223413x_{12} = 27.8373174223413
x13=−12.3925873529074x_{13} = -12.3925873529074
x14=−92.211746210428x_{14} = -92.211746210428
x15=−83.3283456710998x_{15} = -83.3283456710998
x16=36.7068002210725x_{16} = 36.7068002210725
x17=72.224157740075x_{17} = 72.224157740075
x18=81.1069696811089x_{18} = 81.1069696811089
x19=−65.5634956420564x_{19} = -65.5634956420564
x20=18.9821750786416x_{20} = 18.9821750786416
x21=−47.8037102427204x_{21} = -47.8037102427204
x22=−101.095566418709x_{22} = -101.095566418709
x23=−74.4455169192843x_{23} = -74.4455169192843
x24=−21.2025302264653x_{24} = -21.2025302264653
Puntos máximos de la función:
x24=−25.6276971876651x_{24} = -25.6276971876651
x24=50.0216220875817x_{24} = 50.0216220875817
x24=−8.05483051308111x_{24} = -8.05483051308111
x24=32.2709775887511x_{24} = 32.2709775887511
x24=−78.8868476073282x_{24} = -78.8868476073282
x24=58.9015808298421x_{24} = 58.9015808298421
x24=−70.0043858839905x_{24} = -70.0043858839905
x24=−16.7871590134849x_{24} = -16.7871590134849
x24=5.84186222701659x_{24} = 5.84186222701659
x24=23.4069876500919x_{24} = 23.4069876500919
x24=67.7830376469223x_{24} = 67.7830376469223
x24=−87.7699854329339x_{24} = -87.7699854329339
x24=−52.242894420254x_{24} = -52.242894420254
x24=41.144105598611x_{24} = 41.144105598611
x24=−1.05537450400253x_{24} = -1.05537450400253
x24=14.5674907317375x_{24} = 14.5674907317375
x24=−43.3652995706866x_{24} = -43.3652995706866
x24=94.4322181849273x_{24} = 94.4322181849273
x24=85.5486029062939x_{24} = 85.5486029062939
x24=−61.1228994620739x_{24} = -61.1228994620739
x24=−34.4920230298981x_{24} = -34.4920230298981
x24=76.6654793043163x_{24} = 76.6654793043163
x24=−96.6536111584108x_{24} = -96.6536111584108
Decrece en los intervalos
[98.8741692336653,∞)\left[98.8741692336653, \infty\right)
Crece en los intervalos
(−∞,−101.095566418709]\left(-\infty, -101.095566418709\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
(x+1)sin⁡(2x2)2+(x+1)cos⁡(2x2)2+2sin⁡(2x2)−2cos⁡(2x2)=0\frac{\left(x + 1\right) \sin{\left(\frac{\sqrt{2} x}{2} \right)}}{2} + \frac{\left(x + 1\right) \cos{\left(\frac{\sqrt{2} x}{2} \right)}}{2} + \sqrt{2} \sin{\left(\frac{\sqrt{2} x}{2} \right)} - \sqrt{2} \cos{\left(\frac{\sqrt{2} x}{2} \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=4.05374579292121x_{1} = 4.05374579292121
x2=78.9112068225516x_{2} = 78.9112068225516
x3=38.9751214656651x_{3} = 38.9751214656651
x4=105.555999915198x_{4} = 105.555999915198
x5=52.2788807662597x_{5} = 52.2788807662597
x6=8.19698757617941x_{6} = 8.19698757617941
x7=136.64770595186x_{7} = 136.64770595186
x8=−54.5000127889216x_{8} = -54.5000127889216
x9=83.3514579684065x_{9} = 83.3514579684065
x10=61.1539523559803x_{10} = 61.1539523559803
x11=87.791971918382x_{11} = 87.791971918382
x12=34.5446406916175x_{12} = 34.5446406916175
x13=12.5097939402944x_{13} = 12.5097939402944
x14=30.1176519761613x_{14} = 30.1176519761613
x15=−76.692551465808x_{15} = -76.692551465808
x16=25.6958559733325x_{16} = 25.6958559733325
x17=92.2327112087521x_{17} = 92.2327112087521
x18=−72.2529563082306x_{18} = -72.2529563082306
x19=−85.5727754819736x_{19} = -85.5727754819736
x20=−98.8949941177303x_{20} = -98.8949941177303
x21=70.0316894356098x_{21} = 70.0316894356098
x22=43.408060880844x_{22} = 43.408060880844
x23=47.8427956197x_{23} = 47.8427956197
x24=65.5925540321573x_{24} = 65.5925540321573
x25=−67.8137969569567x_{25} = -67.8137969569567
x26=16.8826537404212x_{26} = 16.8826537404212
x27=−143.311078494836x_{27} = -143.311078494836
x28=−94.4540511570912x_{28} = -94.4540511570912
x29=−19.1014566650618x_{29} = -19.1014566650618
x30=−36.765391918438x_{30} = -36.765391918438
x31=21.2822540587397x_{31} = 21.2822540587397
x32=−58.9371844511484x_{32} = -58.9371844511484
x33=−6.2522080294602x_{33} = -6.2522080294602
x34=−32.3381961683913x_{34} = -32.3381961683913
x35=0.443398334876145x_{35} = 0.443398334876145
x36=−10.4094401282718x_{36} = -10.4094401282718
x37=74.4712647261291x_{37} = 74.4712647261291
x38=101.114748448919x_{38} = 101.114748448919
x39=−50.0638693094348x_{39} = -50.0638693094348
x40=−14.7267492968965x_{40} = -14.7267492968965
x41=56.7160069247046x_{41} = 56.7160069247046
x42=−23.5019702167022x_{42} = -23.5019702167022
x43=−63.3751660551827x_{43} = -63.3751660551827
x44=−41.1960157741251x_{44} = -41.1960157741251
x45=−2.60298606603129x_{45} = -2.60298606603129
x46=−45.6290581098304x_{46} = -45.6290581098304
x47=−90.0133014871093x_{47} = -90.0133014871093
x48=96.6736451688094x_{48} = 96.6736451688094
x49=−81.132510224783x_{49} = -81.132510224783
x50=−27.9160849748559x_{50} = -27.9160849748559

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
[105.555999915198,∞)\left[105.555999915198, \infty\right)
Convexa en los intervalos
(−∞,−94.4540511570912]\left(-\infty, -94.4540511570912\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=lim⁡x→−∞((−x−1)sin⁡(2x2)+((−x−1)cos⁡(2x2)−1))y = \lim_{x \to -\infty}\left(\left(- x - 1\right) \sin{\left(\frac{\sqrt{2} x}{2} \right)} + \left(\left(- x - 1\right) \cos{\left(\frac{\sqrt{2} x}{2} \right)} - 1\right)\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=lim⁡x→∞((−x−1)sin⁡(2x2)+((−x−1)cos⁡(2x2)−1))y = \lim_{x \to \infty}\left(\left(- x - 1\right) \sin{\left(\frac{\sqrt{2} x}{2} \right)} + \left(\left(- x - 1\right) \cos{\left(\frac{\sqrt{2} x}{2} \right)} - 1\right)\right)
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función -1 + (-1 - x)*cos((x*sqrt(2))/2) + (-1 - x)*sin((x*sqrt(2))/2), dividida por x con x->+oo y x ->-oo
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=xlim⁡x→−∞((−x−1)sin⁡(2x2)+((−x−1)cos⁡(2x2)−1)x)y = x \lim_{x \to -\infty}\left(\frac{\left(- x - 1\right) \sin{\left(\frac{\sqrt{2} x}{2} \right)} + \left(\left(- x - 1\right) \cos{\left(\frac{\sqrt{2} x}{2} \right)} - 1\right)}{x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞((−x−1)sin⁡(2x2)+((−x−1)cos⁡(2x2)−1)x)y = x \lim_{x \to \infty}\left(\frac{\left(- x - 1\right) \sin{\left(\frac{\sqrt{2} x}{2} \right)} + \left(\left(- x - 1\right) \cos{\left(\frac{\sqrt{2} x}{2} \right)} - 1\right)}{x}\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:
(−x−1)sin⁡(2x2)+((−x−1)cos⁡(2x2)−1)=−(x−1)sin⁡(2x2)+(x−1)cos⁡(2x2)−1\left(- x - 1\right) \sin{\left(\frac{\sqrt{2} x}{2} \right)} + \left(\left(- x - 1\right) \cos{\left(\frac{\sqrt{2} x}{2} \right)} - 1\right) = - \left(x - 1\right) \sin{\left(\frac{\sqrt{2} x}{2} \right)} + \left(x - 1\right) \cos{\left(\frac{\sqrt{2} x}{2} \right)} - 1
- No
(−x−1)sin⁡(2x2)+((−x−1)cos⁡(2x2)−1)=(x−1)sin⁡(2x2)−(x−1)cos⁡(2x2)+1\left(- x - 1\right) \sin{\left(\frac{\sqrt{2} x}{2} \right)} + \left(\left(- x - 1\right) \cos{\left(\frac{\sqrt{2} x}{2} \right)} - 1\right) = \left(x - 1\right) \sin{\left(\frac{\sqrt{2} x}{2} \right)} - \left(x - 1\right) \cos{\left(\frac{\sqrt{2} x}{2} \right)} + 1
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор