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|sin4x|
Trazado el gráfico de la función/ |sin4x|

Gráfico de la función y = |sin4x|

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = |sin(4*x)|
f(x)=∣sin⁡(4x)∣f{\left(x \right)} = \left|{\sin{\left(4 x \right)}}\right| 
f = Abs(sin(4*x))
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:
∣sin⁡(4x)∣=0\left|{\sin{\left(4 x \right)}}\right| = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=0x_{1} = 0
x2=π4x_{2} = \frac{\pi}{4}
Solución numérica
x1=−59.6902604182061x_{1} = -59.6902604182061
x2=68.329640215578x_{2} = 68.329640215578
x3=87.9645943005142x_{3} = 87.9645943005142
x4=−55.7632696012188x_{4} = -55.7632696012188
x5=98.174770424681x_{5} = 98.174770424681
x6=−37.6991118430775x_{6} = -37.6991118430775
x7=−91.8915851175014x_{7} = -91.8915851175014
x8=95.8185759344887x_{8} = 95.8185759344887
x9=−81.6814089933346x_{9} = -81.6814089933346
x10=−33.7721210260903x_{10} = -33.7721210260903
x11=−21.9911485751286x_{11} = -21.9911485751286
x12=−15.707963267949x_{12} = -15.707963267949
x13=−18.0641577581413x_{13} = -18.0641577581413
x14=−27.4889357189107x_{14} = -27.4889357189107
x15=−87.9645943005142x_{15} = -87.9645943005142
x16=72.2566310325652x_{16} = 72.2566310325652
x17=−11.7809724509617x_{17} = -11.7809724509617
x18=25.9181393921158x_{18} = 25.9181393921158
x19=−40.0553063332699x_{19} = -40.0553063332699
x20=3.92699081698724x_{20} = 3.92699081698724
x21=91.8915851175014x_{21} = 91.8915851175014
x22=80.1106126665397x_{22} = 80.1106126665397
x23=6.28318530717959x_{23} = 6.28318530717959
x24=46.3384916404494x_{24} = 46.3384916404494
x25=10.9955742875643x_{25} = 10.9955742875643
x26=−51.8362787842316x_{26} = -51.8362787842316
x27=−99.7455667514759x_{27} = -99.7455667514759
x28=65.9734457253857x_{28} = 65.9734457253857
x29=0x_{29} = 0
x30=−25.1327412287183x_{30} = -25.1327412287183
x31=10.2101761241668x_{31} = 10.2101761241668
x32=11.7809724509617x_{32} = 11.7809724509617
x33=24.3473430653209x_{33} = 24.3473430653209
x34=−73.8274273593601x_{34} = -73.8274273593601
x35=−43.9822971502571x_{35} = -43.9822971502571
x36=96.6039740978861x_{36} = 96.6039740978861
x37=−77.7544181763474x_{37} = -77.7544181763474
x38=54.1924732744239x_{38} = 54.1924732744239
x39=43.9822971502571x_{39} = 43.9822971502571
x40=76.1836218495525x_{40} = 76.1836218495525
x41=−65.9734457253857x_{41} = -65.9734457253857
x42=36.9137136796801x_{42} = 36.9137136796801
x43=69.9004365423729x_{43} = 69.9004365423729
x44=−95.8185759344887x_{44} = -95.8185759344887
x45=−62.0464549083984x_{45} = -62.0464549083984
x46=−84.037603483527x_{46} = -84.037603483527
x47=−72.2566310325652x_{47} = -72.2566310325652
x48=28.2743338823081x_{48} = 28.2743338823081
x49=90.3207887907066x_{49} = 90.3207887907066
x50=21.9911485751286x_{50} = 21.9911485751286
x51=50.2654824574367x_{51} = 50.2654824574367
x52=−80.1106126665397x_{52} = -80.1106126665397
x53=94.2477796076938x_{53} = 94.2477796076938
x54=32.2013246992954x_{54} = 32.2013246992954
x55=47.9092879672443x_{55} = 47.9092879672443
x56=−7.06858347057703x_{56} = -7.06858347057703
x57=−58.1194640914112x_{57} = -58.1194640914112
x58=83.2522053201295x_{58} = 83.2522053201295
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(sin(4*x)).
∣sin⁡(0⋅4)∣\left|{\sin{\left(0 \cdot 4 \right)}}\right|
Resultado:
f(0)=0f{\left(0 \right)} = 0
Punto:
(0, 0)
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
16(−sin⁡(4x)sign⁡(sin⁡(4x))+2cos⁡2(4x)δ(sin⁡(4x)))=016 \left(- \sin{\left(4 x \right)} \operatorname{sign}{\left(\sin{\left(4 x \right)} \right)} + 2 \cos^{2}{\left(4 x \right)} \delta\left(\sin{\left(4 x \right)}\right)\right) = 0
Resolvermos esta ecuación
Soluciones no halladas,
tal vez la función no tenga flexiones
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:
∣sin⁡(4x)∣=∣sin⁡(4x)∣\left|{\sin{\left(4 x \right)}}\right| = \left|{\sin{\left(4 x \right)}}\right|
- Sí
∣sin⁡(4x)∣=−∣sin⁡(4x)∣\left|{\sin{\left(4 x \right)}}\right| = - \left|{\sin{\left(4 x \right)}}\right|
- No
es decir, función
es
par
Gráfico
Gráfico de la función y = |sin4x|
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