In order to find the extrema, we need to solve the equation
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(the derivative equals zero),
and the roots of this equation are the extrema of this function:
$$\frac{d}{d x} f{\left(x \right)} = $$
the first derivative$$- \frac{3^{\left|{x}\right|} \log{\left(3 \right)} \operatorname{sign}{\left(x \right)}}{\left(3^{\left|{x}\right|} - 1\right)^{2}} = 0$$
Solve this equationThe roots of this equation
$$x_{1} = 73.2951886379681$$
$$x_{2} = -50.9855570613729$$
$$x_{3} = -52.9855570613729$$
$$x_{4} = 119.295188637968$$
$$x_{5} = -110.985557061373$$
$$x_{6} = 81.2951886379681$$
$$x_{7} = 83.2951886379681$$
$$x_{8} = -34.9855569831818$$
$$x_{9} = 43.2951886379595$$
$$x_{10} = -42.985557061361$$
$$x_{11} = 67.2951886379681$$
$$x_{12} = 107.295188637968$$
$$x_{13} = -56.9855570613729$$
$$x_{14} = 71.2951886379681$$
$$x_{15} = 109.295188637968$$
$$x_{16} = -86.9855570613729$$
$$x_{17} = 65.2951886379681$$
$$x_{18} = -68.9855570613729$$
$$x_{19} = 111.295188637968$$
$$x_{20} = -46.9855570613727$$
$$x_{21} = -72.9855570613729$$
$$x_{22} = -80.9855570613729$$
$$x_{23} = -48.9855570613729$$
$$x_{24} = 103.295188637968$$
$$x_{25} = -114.985557061373$$
$$x_{26} = -54.9855570613729$$
$$x_{27} = 101.295188637968$$
$$x_{28} = -98.9855570613729$$
$$x_{29} = 37.2951886317662$$
$$x_{30} = 47.2951886379679$$
$$x_{31} = 45.2951886379671$$
$$x_{32} = -62.9855570613729$$
$$x_{33} = 39.295188637279$$
$$x_{34} = -70.9855570613729$$
$$x_{35} = -74.9855570613729$$
$$x_{36} = -112.985557061373$$
$$x_{37} = 25.291892179216$$
$$x_{38} = 63.295188637968$$
$$x_{39} = -116.985557061373$$
$$x_{40} = 31.2951841168205$$
$$x_{41} = -96.9855570613729$$
$$x_{42} = 29.2951479475669$$
$$x_{43} = 55.295188637968$$
$$x_{44} = -76.9855570613729$$
$$x_{45} = -94.9855570613729$$
$$x_{46} = 75.2951886379681$$
$$x_{47} = 27.2948224184264$$
$$x_{48} = 117.295188637968$$
$$x_{49} = -38.9855570604076$$
$$x_{50} = -88.9855570613729$$
$$x_{51} = -60.9855570613729$$
$$x_{52} = -44.9855570613716$$
$$x_{53} = 61.295188637968$$
$$x_{54} = 99.2951886379681$$
$$x_{55} = -58.9855570613729$$
$$x_{56} = -78.9855570613729$$
$$x_{57} = 59.295188637968$$
$$x_{58} = -66.9855570613729$$
$$x_{59} = -82.9855570613729$$
$$x_{60} = 49.295188637968$$
$$x_{61} = -100.985557061373$$
$$x_{62} = 69.2951886379681$$
$$x_{63} = 91.2951886379681$$
$$x_{64} = -102.985557061373$$
$$x_{65} = -40.9855570612656$$
$$x_{66} = -90.9855570613729$$
$$x_{67} = 115.295188637968$$
$$x_{68} = 41.2951886378915$$
$$x_{69} = 77.2951886379681$$
$$x_{70} = -108.985557061373$$
$$x_{71} = 95.2951886379681$$
$$x_{72} = 53.295188637968$$
$$x_{73} = -30.9855507278929$$
$$x_{74} = -64.9855570613729$$
$$x_{75} = -32.9855563576531$$
$$x_{76} = -84.9855570613729$$
$$x_{77} = -106.985557061373$$
$$x_{78} = 57.295188637968$$
$$x_{79} = -118.985557061373$$
$$x_{80} = 97.2951886379681$$
$$x_{81} = -92.9855570613729$$
$$x_{82} = -28.9855000598885$$
$$x_{83} = 105.295188637968$$
$$x_{84} = -36.985557052685$$
$$x_{85} = 89.2951886379681$$
$$x_{86} = 85.2951886379681$$
$$x_{87} = 51.295188637968$$
$$x_{88} = 93.2951886379681$$
$$x_{89} = 33.2951881356184$$
$$x_{90} = -104.985557061373$$
$$x_{91} = -26.9850440346668$$
$$x_{92} = 79.2951886379681$$
$$x_{93} = 35.2951885821514$$
$$x_{94} = 113.295188637968$$
$$x_{95} = 87.2951886379681$$
The values of the extrema at the points:
(73.29518863796805, 1.06981241163236e-35)
(-50.98555706137287, 4.71744713777072e-25)
(-52.98555706137287, 5.24160793085635e-26)
(119.29518863796805, 1.20706293690596e-57)
(-110.98555706137287, 1.11283751841448e-53)
(81.29518863796805, 1.63056304165883e-39)
(83.29518863796805, 1.81173671295425e-40)
(-34.985556983181795, 2.03070648215974e-17)
(43.29518863795954, 2.20264888561953e-21)
(-42.98555706136096, 3.09511706713188e-21)
(67.29518863796805, 7.79893248079989e-33)
(107.29518863796805, 6.41482734252243e-52)
(-56.98555706137287, 6.47112090229179e-28)
(71.29518863796805, 9.62831170469122e-35)
(109.29518863796805, 7.12758593613603e-53)
(-86.98555706137287, 3.14298184504469e-42)
(65.29518863796805, 7.0190392327199e-32)
(-68.98555706137287, 1.21765556332533e-33)
(111.29518863796805, 7.91953992904004e-54)
(-46.98555706137273, 3.82113218159488e-23)
(-72.98555706137287, 1.50327847324115e-35)
(-80.98555706137287, 2.29123376503758e-39)
(-48.98555706137286, 4.24570242399371e-24)
(103.29518863796805, 5.19601014744317e-50)
(-114.98555706137287, 1.37387347952405e-55)
(-54.98555706137287, 5.82400881206261e-27)
(101.29518863796805, 4.67640913269885e-49)
(-98.98555706137287, 5.91407483623711e-48)
(37.2951886317662, 1.60573104854215e-18)
(47.29518863796795, 2.71931961185085e-23)
(45.2951886379671, 2.44738765066804e-22)
(-62.98555706137287, 8.87670905664169e-31)
(39.295188637278955, 1.78414559868582e-19)
(-70.98555706137287, 1.35295062591704e-34)
(-74.98555706137287, 1.67030941471239e-36)
(-112.98555706137287, 1.23648613157165e-54)
(25.291892179216028, 8.5644734861644e-13)
(63.295188637968046, 6.31713530944796e-31)
(-116.98555706137287, 1.52652608836006e-56)
(31.295184116820504, 1.17058374067283e-15)
(-96.98555706137287, 5.3226673526134e-47)
(29.295147947566942, 1.05356723030698e-14)
(55.295188637968046, 4.14467247652881e-27)
(-76.98555706137287, 1.85589934968044e-37)
(-94.98555706137287, 4.79040061735206e-46)
(75.29518863796805, 1.18868045736929e-36)
(27.294822418426417, 9.48549676742939e-14)
(117.29518863796805, 1.08635664321537e-56)
(-38.98555706040755, 2.50704482700277e-19)
(-88.98555706137287, 3.49220205004965e-43)
(-60.98555706137287, 7.98903815097752e-30)
(-44.98555706137155, 3.43901896343985e-22)
(61.295188637968046, 5.68542177850316e-30)
(99.29518863796805, 4.20876821942897e-48)
(-58.98555706137287, 7.19013433587977e-29)
(-78.98555706137287, 2.06211038853382e-38)
(59.295188637968046, 5.11687960065285e-29)
(-66.98555706137287, 1.0958900069928e-32)
(-82.98555706137287, 2.5458152944862e-40)
(49.29518863796804, 3.02146623538952e-24)
(-100.98555706137287, 6.57119426248568e-49)
(69.29518863796805, 8.6654805342221e-34)
(91.29518863796805, 2.76137282876734e-44)
(-102.98555706137287, 7.30132695831742e-50)
(-40.98555706126562, 2.78560536071047e-20)
(-90.98555706137287, 3.88022450005517e-44)
(115.29518863796805, 9.77720978893832e-56)
(41.295188637891485, 1.98238399720579e-20)
(77.29518863796805, 1.32075606374365e-37)
(-108.98555706137287, 1.00155376657303e-52)
(95.29518863796805, 3.40910225773746e-46)
(53.295188637968046, 3.73020522887593e-26)
(-30.985550727892903, 1.64488355437609e-15)
(-64.98555706137287, 9.86301006293521e-32)
(-32.9855563576531, 1.82763708992023e-16)
(-84.98555706137287, 2.82868366054022e-41)
(-106.98555706137287, 9.01398389915731e-52)
(57.295188637968046, 4.60519164058756e-28)
(-118.98555706137287, 1.69614009817784e-57)
(97.29518863796805, 3.78789139748607e-47)
(-92.98555706137287, 4.31136055561685e-45)
(-28.98550005988846, 1.48047760667926e-14)
(105.29518863796805, 5.77334460827019e-51)
(-36.985557052684975, 2.25634036344554e-18)
(89.29518863796805, 2.48523554589061e-43)
(85.29518863796805, 2.01304079217139e-41)
(51.295188637968046, 3.35718470598833e-25)
(93.29518863796805, 3.06819203196372e-45)
(33.295188135618424, 1.30064285826562e-16)
(-104.98555706137287, 8.11258550924158e-51)
(-26.98504403466683, 1.33309755383065e-13)
(79.29518863796805, 1.46750673749295e-38)
(35.295188582151425, 1.44515802245975e-17)
(113.29518863796805, 8.79948881004449e-55)
(87.29518863796805, 2.23671199130155e-42)
Intervals of increase and decrease of the function:Let's find intervals where the function increases and decreases, as well as minima and maxima of the function, for this let's look how the function behaves itself in the extremas and at the slightest deviation from:
The function has no minima
The function has no maxima
Decreasing at the entire real axis