Sr Examen

Otras calculadoras

Trazado el gráfico de la función/ abs(cos(abs(2*x-pi/6)))

Gráfico de la función y = abs(cos(abs(2*x-pi/6)))

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
       |   /|      pi|\|
f(x) = |cos||2*x - --|||
       |   \|      6 |/|
f(x)=∣cos⁡(∣2x−π6∣)∣f{\left(x \right)} = \left|{\cos{\left(\left|{2 x - \frac{\pi}{6}}\right| \right)}}\right| 
f = Abs(cos(|2*x - pi/6|))
Gráfico de la función
02468-8-6-4-2-101002
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:
∣cos⁡(∣2x−π6∣)∣=0\left|{\cos{\left(\left|{2 x - \frac{\pi}{6}}\right| \right)}}\right| = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=−π6x_{1} = - \frac{\pi}{6}
x2=π3x_{2} = \frac{\pi}{3}
Solución numérica
x1=−75.9218224617533x_{1} = -75.9218224617533
x2=−47.6474885794452x_{2} = -47.6474885794452
x3=34.0339204138894x_{3} = 34.0339204138894
x4=71.733032256967x_{4} = 71.733032256967
x5=−90.0589894029074x_{5} = -90.0589894029074
x6=−24.0855436775217x_{6} = -24.0855436775217
x7=40.317105721069x_{7} = 40.317105721069
x8=78.0162175641465x_{8} = 78.0162175641465
x9=−46.0766922526503x_{9} = -46.0766922526503
x10=−16.2315620435473x_{10} = -16.2315620435473
x11=−60.2138591938044x_{11} = -60.2138591938044
x12=−38.2227106186758x_{12} = -38.2227106186758
x13=84.2994028713261x_{13} = 84.2994028713261
x14=145.560459616327x_{14} = 145.560459616327
x15=−83.7758040957278x_{15} = -83.7758040957278
x16=32.4631240870945x_{16} = 32.4631240870945
x17=131.423292675173x_{17} = 131.423292675173
x18=70.162235930172x_{18} = 70.162235930172
x19=−17.8023583703422x_{19} = -17.8023583703422
x20=101.57816246607x_{20} = 101.57816246607
x21=−5.23598775598299x_{21} = -5.23598775598299
x22=48.1710873550435x_{22} = 48.1710873550435
x23=−61.7846555205993x_{23} = -61.7846555205993
x24=18.3259571459405x_{24} = 18.3259571459405
x25=76.4454212373516x_{25} = 76.4454212373516
x26=−170.169602069447x_{26} = -170.169602069447
x27=3535.33893283971x_{27} = 3535.33893283971
x28=−77.4926187885482x_{28} = -77.4926187885482
x29=−82.2050077689329x_{29} = -82.2050077689329
x30=−11.5191730631626x_{30} = -11.5191730631626
x31=90.5825881785057x_{31} = 90.5825881785057
x32=−55.5014702134197x_{32} = -55.5014702134197
x33=−2.0943951023932x_{33} = -2.0943951023932
x34=−39.7935069454707x_{34} = -39.7935069454707
x35=−25.6563400043166x_{35} = -25.6563400043166
x36=74.8746249105567x_{36} = 74.8746249105567
x37=−99.4837673636768x_{37} = -99.4837673636768
x38=26.1799387799149x_{38} = 26.1799387799149
x39=12.0427718387609x_{39} = 12.0427718387609
x40=−33.5103216382911x_{40} = -33.5103216382911
x41=54.4542726622231x_{41} = 54.4542726622231
x42=4.18879020478639x_{42} = 4.18879020478639
x43=19.8967534727354x_{43} = 19.8967534727354
x44=98.4365698124802x_{44} = 98.4365698124802
x45=49.7418836818384x_{45} = 49.7418836818384
x46=27.7507351067098x_{46} = 27.7507351067098
x47=−96.342174710087x_{47} = -96.342174710087
x48=10.471975511966x_{48} = 10.471975511966
x49=62.3082542961976x_{49} = 62.3082542961976
x50=92.1533845053006x_{50} = 92.1533845053006
x51=100.007366139275x_{51} = 100.007366139275
x52=−68.0678408277789x_{52} = -68.0678408277789
x53=−69.6386371545737x_{53} = -69.6386371545737
x54=93.7241808320955x_{54} = 93.7241808320955
x55=85.870199198121x_{55} = 85.870199198121
x56=−3.66519142918809x_{56} = -3.66519142918809
x57=41.8879020478639x_{57} = 41.8879020478639
x58=56.025068989018x_{58} = 56.025068989018
x59=63.8790506229925x_{59} = 63.8790506229925
x60=5.75958653158129x_{60} = 5.75958653158129
x61=−91.6297857297023x_{61} = -91.6297857297023
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 Abs(cos(|2*x - pi/6|)).
∣cos⁡(∣−π6+0⋅2∣)∣\left|{\cos{\left(\left|{- \frac{\pi}{6} + 0 \cdot 2}\right| \right)}}\right|
Resultado:
f(0)=32f{\left(0 \right)} = \frac{\sqrt{3}}{2}
Punto:
(0, sqrt(3)/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
−2sin⁡(∣2x−π6∣)sign⁡(2x−π6)sign⁡(cos⁡(∣2x−π6∣))=0- 2 \sin{\left(\left|{2 x - \frac{\pi}{6}}\right| \right)} \operatorname{sign}{\left(2 x - \frac{\pi}{6} \right)} \operatorname{sign}{\left(\cos{\left(\left|{2 x - \frac{\pi}{6}}\right| \right)} \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=61.5228561328001x_{1} = 61.5228561328001
x2=−2.87979326579064x_{2} = -2.87979326579064
x3=−95.5567765466895x_{3} = -95.5567765466895
x4=−65.7116463375865x_{4} = -65.7116463375865
x5=6.54498469497874x_{5} = 6.54498469497874
x6=80.3724120543389x_{6} = 80.3724120543389
x7=−1.30899693899575x_{7} = -1.30899693899575
x8=−71.9948316447661x_{8} = -71.9948316447661
x9=30.1069295969022x_{9} = 30.1069295969022
x10=53.6688744988256x_{10} = 53.6688744988256
x11=−78.2780169519457x_{11} = -78.2780169519457
x12=−21.7293491873294x_{12} = -21.7293491873294
x13=−37.4373124552784x_{13} = -37.4373124552784
x14=−81.4196096055355x_{14} = -81.4196096055355
x15=−29.5833308213039x_{15} = -29.5833308213039
x16=39.5317075576716x_{16} = 39.5317075576716
x17=−56.2868683768171x_{17} = -56.2868683768171
x18=−87.7027949127151x_{18} = -87.7027949127151
x19=23.8237442897226x_{19} = 23.8237442897226
x20=36.3901149040818x_{20} = 36.3901149040818
x21=50.5272818452358x_{21} = 50.5272818452358
x22=28.5361332701073x_{22} = 28.5361332701073
x23=−51.5744793964324x_{23} = -51.5744793964324
x24=31.6777259236971x_{24} = 31.6777259236971
x25=−50.0036830696375x_{25} = -50.0036830696375
x26=−23.3001455141243x_{26} = -23.3001455141243
x27=−48.4328867428426x_{27} = -48.4328867428426
x28=14.3989663289532x_{28} = 14.3989663289532
x29=−93.9859802198946x_{29} = -93.9859802198946
x30=74.0892267471593x_{30} = 74.0892267471593
x31=83.5140047079287x_{31} = 83.5140047079287
x32=−67.2824426643814x_{32} = -67.2824426643814
x33=44.2440965380563x_{33} = 44.2440965380563
x34=−100.269165527074x_{34} = -100.269165527074
x35=78.801615727544x_{35} = 78.801615727544
x36=−89.27359123951x_{36} = -89.27359123951
x37=−73.565627971561x_{37} = -73.565627971561
x38=100.792764302673x_{38} = 100.792764302673
x39=−7.59218224617533x_{39} = -7.59218224617533
x40=9.68657734856853x_{40} = 9.68657734856853
x41=59.9520598060052x_{41} = 59.9520598060052
x42=75.6600230739542x_{42} = 75.6600230739542
x43=0.261799387799149x_{43} = 0.261799387799149
x44=67.8060414399797x_{44} = 67.8060414399797
x45=−26.4417381677141x_{45} = -26.4417381677141
x46=64.6644487863899x_{46} = 64.6644487863899
x47=−12.30457122656x_{47} = -12.30457122656
x48=−64.1408500107916x_{48} = -64.1408500107916
x49=−86.1319985859202x_{49} = -86.1319985859202
x50=−13.8753675533549x_{50} = -13.8753675533549
x51=−59.4284610304069x_{51} = -59.4284610304069
x52=−43.720497762458x_{52} = -43.720497762458
x53=−45.2912940892529x_{53} = -45.2912940892529
x54=22.2529479629277x_{54} = 22.2529479629277
x55=−70.4240353179712x_{55} = -70.4240353179712
x56=−28.012534494509x_{56} = -28.012534494509
x57=37.9609112308767x_{57} = 37.9609112308767
x58=−1801.44158744595x_{58} = -1801.44158744595
x59=−20.1585528605345x_{59} = -20.1585528605345
x60=99.2219679758776x_{60} = 99.2219679758776
x61=−79.8488132787406x_{61} = -79.8488132787406
x62=−15.4461638801498x_{62} = -15.4461638801498
x63=−4.45058959258554x_{63} = -4.45058959258554
x64=−35.8665161284835x_{64} = -35.8665161284835
x65=15.9697626557481x_{65} = 15.9697626557481
x66=66.2352451131848x_{66} = 66.2352451131848
x67=−34.2957198016886x_{67} = -34.2957198016886
x68=45.8148928648512x_{68} = 45.8148928648512
x69=97.6511716490827x_{69} = 97.6511716490827
x70=8.11578102177363x_{70} = 8.11578102177363
x71=89.7971900151083x_{71} = 89.7971900151083
x72=105.505153283057x_{72} = 105.505153283057
x73=−92.4151838930998x_{73} = -92.4151838930998
x74=42.6733002112614x_{74} = 42.6733002112614
x75=−6.02138591938044x_{75} = -6.02138591938044
x76=−57.857664703612x_{76} = -57.857664703612
x77=17.540558982543x_{77} = 17.540558982543
x78=81.9432083811338x_{78} = 81.9432083811338
x79=96.0803753222878x_{79} = 96.0803753222878
x80=72.5184304203644x_{80} = 72.5184304203644
x81=52.0980781720307x_{81} = 52.0980781720307
x82=88.2263936883134x_{82} = 88.2263936883134
x83=58.3812634792103x_{83} = 58.3812634792103
x84=1.83259571459405x_{84} = 1.83259571459405
x85=−42.1497014356631x_{85} = -42.1497014356631
x86=20.6821516361328x_{86} = 20.6821516361328
x87=94.5095789954929x_{87} = 94.5095789954929
x88=86.6555973615185x_{88} = 86.6555973615185
Signos de extremos en los puntos:
                         /                 pi\ 
(61.522856132800115, -cos|123.0457122656 - --|)
                         \                 6 / 

                        /                   pi\ 
(-2.879793265790644, cos|5.75958653158129 + --|)
                        \                   6 / 

                         /                   pi\ 
(-95.55677654668955, -cos|191.113553093379 + --|)
                         \                   6 / 

                        /                   pi\ 
(-65.71164633758652, cos|131.423292675173 + --|)
                        \                   6 / 

                       /                   pi\ 
(6.544984694978736, cos|13.0899693899575 - --|)
                       \                   6 / 

                        /                   pi\ 
(80.37241205433888, -cos|160.744824108678 - --|)
                        \                   6 / 

                          /                   pi\ 
(-1.3089969389957472, -cos|2.61799387799149 + --|)
                          \                   6 / 

                       /                   pi\ 
(-71.9948316447661, cos|143.989663289532 + --|)
                       \                   6 / 

                         /                   pi\ 
(30.106929596902184, -cos|60.2138591938044 - --|)
                         \                   6 / 

                       /                   pi\ 
(53.66887449882564, cos|107.337748997651 - --|)
                       \                   6 / 

                        /                   pi\ 
(-78.27801695194569, cos|156.556033903891 + --|)
                        \                   6 / 

                         /                   pi\ 
(-21.729349187329404, cos|43.4586983746588 + --|)
                         \                   6 / 

                        /                   pi\ 
(-37.43731245527837, cos|74.8746249105567 + --|)
                        \                   6 / 

                        /                   pi\ 
(-81.41960960553547, cos|162.839219211071 + --|)
                        \                   6 / 

                          /                   pi\ 
(-29.583330821303885, -cos|59.1666616426078 + --|)
                          \                   6 / 

                        /                   pi\ 
(39.53170755767157, -cos|79.0634151153431 - --|)
                        \                   6 / 

                        /                   pi\ 
(-56.28686837681713, cos|112.573736753634 + --|)
                        \                   6 / 

                        /                  pi\ 
(-87.70279491271506, cos|175.40558982543 + --|)
                        \                  6 / 

                         /                   pi\ 
(23.823744289722598, -cos|47.6474885794452 - --|)
                         \                   6 / 

                        /                   pi\ 
(36.39011490408177, -cos|72.7802298081635 - --|)
                        \                   6 / 

                       /                   pi\ 
(50.52728184523584, cos|101.054563690472 - --|)
                       \                   6 / 

                       /                   pi\ 
(28.53613327010729, cos|57.0722665402146 - --|)
                       \                   6 / 

                         /                   pi\ 
(-51.57447939643244, -cos|103.148958792865 + --|)
                         \                   6 / 

                        /                   pi\ 
(31.677725923697082, cos|63.3554518473942 - --|)
                        \                   6 / 

                        /                   pi\ 
(-50.00368306963754, cos|100.007366139275 + --|)
                        \                   6 / 

                        /                   pi\ 
(-23.3001455141243, -cos|46.6002910282486 + --|)
                        \                   6 / 

                         /                   pi\ 
(-48.43288674284265, -cos|96.8657734856853 + --|)
                         \                   6 / 

                         /                   pi\ 
(14.398966328953218, -cos|28.7979326579064 - --|)
                         \                   6 / 

                        /                   pi\ 
(-93.98598021989464, cos|187.971960439789 + --|)
                        \                   6 / 

                        /                   pi\ 
(74.08922674715929, -cos|148.178453494319 - --|)
                        \                   6 / 

                        /                   pi\ 
(83.51400470792866, -cos|167.028009415857 - --|)
                        \                   6 / 

                        /                   pi\ 
(-67.2824426643814, -cos|134.564885328763 + --|)
                        \                   6 / 

                        /                   pi\ 
(44.244096538056255, cos|88.4881930761125 - --|)
                        \                   6 / 

                         /                   pi\ 
(-100.26916552707424, cos|200.538331054148 + --|)
                         \                   6 / 

                       /                   pi\ 
(78.80161572754398, cos|157.603231455088 - --|)
                       \                   6 / 

                         /                  pi\ 
(-89.27359123950995, -cos|178.54718247902 + --|)
                         \                  6 / 

                         /                   pi\ 
(-73.56562797156099, -cos|147.131255943122 + --|)
                         \                   6 / 

                        /                   pi\ 
(100.79276430267254, cos|201.585528605345 - --|)
                        \                   6 / 

                         /                   pi\ 
(-7.592182246175334, -cos|15.1843644923507 + --|)
                         \                   6 / 

                       /                   pi\ 
(9.686577348568528, cos|19.3731546971371 - --|)
                       \                   6 / 

                        /                  pi\ 
(59.952059806005224, cos|119.90411961201 - --|)
                        \                  6 / 

                       /                   pi\ 
(75.66002307395419, cos|151.320046147908 - --|)
                       \                   6 / 

                         /                    pi\ 
(0.26179938779914946, cos|0.523598775598299 - --|)
                         \                    6 / 

                        /                   pi\ 
(67.80604143997971, -cos|135.612082879959 - --|)
                        \                   6 / 

                          /                   pi\ 
(-26.441738167714092, -cos|52.8834763354282 + --|)
                          \                   6 / 

                        /                  pi\ 
(64.66444878638991, -cos|129.32889757278 - --|)
                        \                  6 / 

                         /                 pi\ 
(-12.304571226560023, cos|24.60914245312 + --|)
                         \                 6 / 

                         /                   pi\ 
(-64.14085001079161, -cos|128.281700021583 + --|)
                         \                   6 / 

                         /                  pi\ 
(-86.13199858592016, -cos|172.26399717184 + --|)
                         \                  6 / 

                         /                   pi\ 
(-13.87536755335492, -cos|27.7507351067098 + --|)
                         \                   6 / 

                        /                   pi\ 
(-59.42846103040692, cos|118.856922060814 + --|)
                        \                   6 / 

                        /                   pi\ 
(-43.72049776245795, cos|87.4409955249159 + --|)
                        \                   6 / 

                         /                   pi\ 
(-45.29129408925285, -cos|90.5825881785057 + --|)
                         \                   6 / 

                        /                   pi\ 
(22.252947962927703, cos|44.5058959258554 - --|)
                        \                   6 / 

                        /                   pi\ 
(-70.4240353179712, -cos|140.848070635942 + --|)
                        \                   6 / 

                        /                  pi\ 
(-28.01253449450899, cos|56.025068989018 + --|)
                        \                  6 / 

                       /                   pi\ 
(37.96091123087667, cos|75.9218224617533 - --|)
                       \                   6 / 

                          /                   pi\ 
(-1801.4415874459473, -cos|3602.88317489189 + --|)
                          \                   6 / 

                          /                  pi\ 
(-20.158552860534506, -cos|40.317105721069 + --|)
                          \                  6 / 

                        /                   pi\ 
(99.22196797587763, -cos|198.443935951755 - --|)
                        \                   6 / 

                         /                   pi\ 
(-79.84881327874058, -cos|159.697626557481 + --|)
                         \                   6 / 

                         /                   pi\ 
(-15.446163880149816, cos|30.8923277602996 + --|)
                         \                   6 / 

                          /                   pi\ 
(-4.4505895925855405, -cos|8.90117918517108 + --|)
                          \                   6 / 

                          /                  pi\ 
(-35.866516128483475, -cos|71.733032256967 + --|)
                          \                  6 / 

                        /                   pi\ 
(15.969762655748116, cos|31.9395253114962 - --|)
                        \                   6 / 

                      /                  pi\ 
(66.2352451131848, cos|132.47049022637 - --|)
                      \                  6 / 

                        /                   pi\ 
(-34.29571980168858, cos|68.5914396033772 + --|)
                        \                   6 / 

                        /                   pi\ 
(45.81489286485115, -cos|91.6297857297023 - --|)
                        \                   6 / 

                       /                   pi\ 
(97.65117164908274, cos|195.302343298165 - --|)
                       \                   6 / 

                        /                   pi\ 
(8.115781021773632, -cos|16.2315620435473 - --|)
                        \                   6 / 

                        /                   pi\ 
(89.79719001510826, -cos|179.594380030217 - --|)
                        \                   6 / 

                         /                   pi\ 
(105.50515328305723, -cos|211.010306566114 - --|)
                         \                   6 / 

                         /                 pi\ 
(-92.41518389309975, -cos|184.8303677862 + --|)
                         \                 6 / 

                         /                   pi\ 
(42.673300211261356, -cos|85.3466004225227 - --|)
                         \                   6 / 

                        /                   pi\ 
(-6.021385919380437, cos|12.0427718387609 + --|)
                        \                   6 / 

                         /                   pi\ 
(-57.85766470361202, -cos|115.715329407224 + --|)
                         \                   6 / 

                        /                  pi\ 
(17.54055898254301, -cos|35.081117965086 - --|)
                        \                  6 / 

                       /                   pi\ 
(81.94320838113377, cos|163.886416762268 - --|)
                       \                   6 / 

                        /                   pi\ 
(96.08037532228785, -cos|192.160750644576 - --|)
                        \                   6 / 

                      /                   pi\ 
(72.5184304203644, cos|145.036860840729 - --|)
                      \                   6 / 

                        /                   pi\ 
(52.09807817203074, -cos|104.196156344061 - --|)
                        \                   6 / 

                       /                   pi\ 
(88.22639368831337, cos|176.452787376627 - --|)
                       \                   6 / 

                         /                   pi\ 
(58.381263479210325, -cos|116.762526958421 - --|)
                         \                   6 / 

                         /                   pi\ 
(1.8325957145940461, -cos|3.66519142918809 - --|)
                         \                   6 / 

                         /                   pi\ 
(-42.14970143566306, -cos|84.2994028713261 + --|)
                         \                   6 / 

                         /                   pi\ 
(20.682151636132804, -cos|41.3643032722656 - --|)
                         \                   6 / 

                       /                   pi\ 
(94.50957899549294, cos|189.019157990986 - --|)
                       \                   6 / 

                        /                   pi\ 
(86.65559736151846, -cos|173.311194723037 - --|)
                        \                   6 /


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:
La función no tiene puntos mínimos
Puntos máximos de la función:
x88=61.5228561328001x_{88} = 61.5228561328001
x88=−2.87979326579064x_{88} = -2.87979326579064
x88=−95.5567765466895x_{88} = -95.5567765466895
x88=−65.7116463375865x_{88} = -65.7116463375865
x88=6.54498469497874x_{88} = 6.54498469497874
x88=80.3724120543389x_{88} = 80.3724120543389
x88=−1.30899693899575x_{88} = -1.30899693899575
x88=−71.9948316447661x_{88} = -71.9948316447661
x88=30.1069295969022x_{88} = 30.1069295969022
x88=53.6688744988256x_{88} = 53.6688744988256
x88=−78.2780169519457x_{88} = -78.2780169519457
x88=−21.7293491873294x_{88} = -21.7293491873294
x88=−37.4373124552784x_{88} = -37.4373124552784
x88=−81.4196096055355x_{88} = -81.4196096055355
x88=−29.5833308213039x_{88} = -29.5833308213039
x88=39.5317075576716x_{88} = 39.5317075576716
x88=−56.2868683768171x_{88} = -56.2868683768171
x88=−87.7027949127151x_{88} = -87.7027949127151
x88=23.8237442897226x_{88} = 23.8237442897226
x88=36.3901149040818x_{88} = 36.3901149040818
x88=50.5272818452358x_{88} = 50.5272818452358
x88=28.5361332701073x_{88} = 28.5361332701073
x88=−51.5744793964324x_{88} = -51.5744793964324
x88=31.6777259236971x_{88} = 31.6777259236971
x88=−50.0036830696375x_{88} = -50.0036830696375
x88=−23.3001455141243x_{88} = -23.3001455141243
x88=−48.4328867428426x_{88} = -48.4328867428426
x88=14.3989663289532x_{88} = 14.3989663289532
x88=−93.9859802198946x_{88} = -93.9859802198946
x88=74.0892267471593x_{88} = 74.0892267471593
x88=83.5140047079287x_{88} = 83.5140047079287
x88=−67.2824426643814x_{88} = -67.2824426643814
x88=44.2440965380563x_{88} = 44.2440965380563
x88=−100.269165527074x_{88} = -100.269165527074
x88=78.801615727544x_{88} = 78.801615727544
x88=−89.27359123951x_{88} = -89.27359123951
x88=−73.565627971561x_{88} = -73.565627971561
x88=100.792764302673x_{88} = 100.792764302673
x88=−7.59218224617533x_{88} = -7.59218224617533
x88=9.68657734856853x_{88} = 9.68657734856853
x88=59.9520598060052x_{88} = 59.9520598060052
x88=75.6600230739542x_{88} = 75.6600230739542
x88=0.261799387799149x_{88} = 0.261799387799149
x88=67.8060414399797x_{88} = 67.8060414399797
x88=−26.4417381677141x_{88} = -26.4417381677141
x88=64.6644487863899x_{88} = 64.6644487863899
x88=−12.30457122656x_{88} = -12.30457122656
x88=−64.1408500107916x_{88} = -64.1408500107916
x88=−86.1319985859202x_{88} = -86.1319985859202
x88=−13.8753675533549x_{88} = -13.8753675533549
x88=−59.4284610304069x_{88} = -59.4284610304069
x88=−43.720497762458x_{88} = -43.720497762458
x88=−45.2912940892529x_{88} = -45.2912940892529
x88=22.2529479629277x_{88} = 22.2529479629277
x88=−70.4240353179712x_{88} = -70.4240353179712
x88=−28.012534494509x_{88} = -28.012534494509
x88=37.9609112308767x_{88} = 37.9609112308767
x88=−1801.44158744595x_{88} = -1801.44158744595
x88=−20.1585528605345x_{88} = -20.1585528605345
x88=99.2219679758776x_{88} = 99.2219679758776
x88=−79.8488132787406x_{88} = -79.8488132787406
x88=−15.4461638801498x_{88} = -15.4461638801498
x88=−4.45058959258554x_{88} = -4.45058959258554
x88=−35.8665161284835x_{88} = -35.8665161284835
x88=15.9697626557481x_{88} = 15.9697626557481
x88=66.2352451131848x_{88} = 66.2352451131848
x88=−34.2957198016886x_{88} = -34.2957198016886
x88=45.8148928648512x_{88} = 45.8148928648512
x88=97.6511716490827x_{88} = 97.6511716490827
x88=8.11578102177363x_{88} = 8.11578102177363
x88=89.7971900151083x_{88} = 89.7971900151083
x88=105.505153283057x_{88} = 105.505153283057
x88=−92.4151838930998x_{88} = -92.4151838930998
x88=42.6733002112614x_{88} = 42.6733002112614
x88=−6.02138591938044x_{88} = -6.02138591938044
x88=−57.857664703612x_{88} = -57.857664703612
x88=17.540558982543x_{88} = 17.540558982543
x88=81.9432083811338x_{88} = 81.9432083811338
x88=96.0803753222878x_{88} = 96.0803753222878
x88=72.5184304203644x_{88} = 72.5184304203644
x88=52.0980781720307x_{88} = 52.0980781720307
x88=88.2263936883134x_{88} = 88.2263936883134
x88=58.3812634792103x_{88} = 58.3812634792103
x88=1.83259571459405x_{88} = 1.83259571459405
x88=−42.1497014356631x_{88} = -42.1497014356631
x88=20.6821516361328x_{88} = 20.6821516361328
x88=94.5095789954929x_{88} = 94.5095789954929
x88=86.6555973615185x_{88} = 86.6555973615185
Decrece en los intervalos
(−∞,−1801.44158744595]\left(-\infty, -1801.44158744595\right]
Crece en los intervalos
[105.505153283057,∞)\left[105.505153283057, \infty\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
4(2sin⁡2(∣2x−π6∣)δ(cos⁡(∣2x−π6∣))sign⁡2(2x−π6)−2sin⁡(∣2x−π6∣)δ(2x−π6)sign⁡(cos⁡(∣2x−π6∣))−cos⁡(∣2x−π6∣)sign⁡2(2x−π6)sign⁡(cos⁡(∣2x−π6∣)))=04 \left(2 \sin^{2}{\left(\left|{2 x - \frac{\pi}{6}}\right| \right)} \delta\left(\cos{\left(\left|{2 x - \frac{\pi}{6}}\right| \right)}\right) \operatorname{sign}^{2}{\left(2 x - \frac{\pi}{6} \right)} - 2 \sin{\left(\left|{2 x - \frac{\pi}{6}}\right| \right)} \delta\left(2 x - \frac{\pi}{6}\right) \operatorname{sign}{\left(\cos{\left(\left|{2 x - \frac{\pi}{6}}\right| \right)} \right)} - \cos{\left(\left|{2 x - \frac{\pi}{6}}\right| \right)} \operatorname{sign}^{2}{\left(2 x - \frac{\pi}{6} \right)} \operatorname{sign}{\left(\cos{\left(\left|{2 x - \frac{\pi}{6}}\right| \right)} \right)}\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→−∞∣cos⁡(∣2x−π6∣)∣=∣⟨−1,1⟩∣\lim_{x \to -\infty} \left|{\cos{\left(\left|{2 x - \frac{\pi}{6}}\right| \right)}}\right| = \left|{\left\langle -1, 1\right\rangle}\right|
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=∣⟨−1,1⟩∣y = \left|{\left\langle -1, 1\right\rangle}\right|
lim⁡x→∞∣cos⁡(∣2x−π6∣)∣=∣⟨−1,1⟩∣\lim_{x \to \infty} \left|{\cos{\left(\left|{2 x - \frac{\pi}{6}}\right| \right)}}\right| = \left|{\left\langle -1, 1\right\rangle}\right|
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=∣⟨−1,1⟩∣y = \left|{\left\langle -1, 1\right\rangle}\right|
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función Abs(cos(|2*x - pi/6|)), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(∣cos⁡(∣2x−π6∣)∣x)=0\lim_{x \to -\infty}\left(\frac{\left|{\cos{\left(\left|{2 x - \frac{\pi}{6}}\right| \right)}}\right|}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞(∣cos⁡(∣2x−π6∣)∣x)=0\lim_{x \to \infty}\left(\frac{\left|{\cos{\left(\left|{2 x - \frac{\pi}{6}}\right| \right)}}\right|}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la izquierda
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:
∣cos⁡(∣2x−π6∣)∣=∣cos⁡(4x2+2πx3+π236)∣\left|{\cos{\left(\left|{2 x - \frac{\pi}{6}}\right| \right)}}\right| = \left|{\cos{\left(\sqrt{4 x^{2} + \frac{2 \pi x}{3} + \frac{\pi^{2}}{36}} \right)}}\right|
- No
∣cos⁡(∣2x−π6∣)∣=−∣cos⁡(4x2+2πx3+π236)∣\left|{\cos{\left(\left|{2 x - \frac{\pi}{6}}\right| \right)}}\right| = - \left|{\cos{\left(\sqrt{4 x^{2} + \frac{2 \pi x}{3} + \frac{\pi^{2}}{36}} \right)}}\right|
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор