Gráfico de la función y = log(2)log(2-x)(2-x)^x

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
$$\left(2 - x\right)^{x} \left(- \frac{x}{2 - x} + \log{\left(2 - x \right)}\right) \log{\left(2 \right)} \log{\left(2 - x \right)} - \frac{\left(2 - x\right)^{x} \log{\left(2 \right)}}{2 - x} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = -85.7494234057424$$
$$x_{2} = -58.0620620163045$$
$$x_{3} = -23.135064085223$$
$$x_{4} = -103.615853087298$$
$$x_{5} = -0.0151512050529408$$
$$x_{6} = -60.0330103907321$$
$$x_{7} = -65.9536307114313$$
$$x_{8} = -67.9294386091676$$
$$x_{9} = -56.092602232825$$
$$x_{10} = -69.9062434542869$$
$$x_{11} = -79.8029966641312$$
$$x_{12} = -38.4656685275568$$
$$x_{13} = -21.2744419848544$$
$$x_{14} = -17.634316438267$$
$$x_{15} = -14.1819390643894$$
$$x_{16} = -99.6426035859777$$
$$x_{17} = -25.0144657776038$$
$$x_{18} = -34.5864665746434$$
$$x_{19} = -30.7310289506005$$
$$x_{20} = -75.841973969979$$
$$x_{21} = -101.629046071212$$
$$x_{22} = -97.6565438048725$$
$$x_{23} = -36.5235310881045$$
$$x_{24} = -87.7327215399839$$
$$x_{25} = -15.8754455820524$$
$$x_{26} = -77.8221315349043$$
$$x_{27} = -89.7165441896893$$
$$x_{28} = -19.4381477900808$$
$$x_{29} = -73.862571272917$$
$$x_{30} = -91.7008630069666$$
$$x_{31} = -54.1247695205809$$
$$x_{32} = -48.232725553682$$
$$x_{33} = -32.6552934250717$$
$$x_{34} = -63.9788973586082$$
$$x_{35} = -95.6708862218105$$
$$x_{36} = -44.3164106924221$$
$$x_{37} = -52.1587213646046$$
$$x_{38} = -46.2732238251541$$
$$x_{39} = -42.3626119238742$$
$$x_{40} = -62.0053250195045$$
$$x_{41} = -71.8839753780007$$
$$x_{42} = -40.412212007351$$
$$x_{43} = -12.5900575066031$$
$$x_{44} = -50.1946377617752$$
$$x_{45} = -26.9087189574725$$
$$x_{46} = -83.7666805001943$$
$$x_{47} = -81.7845261640393$$
$$x_{48} = -28.8149559927595$$
$$x_{49} = -93.6856517784999$$
Signos de extremos en los puntos:

(-85.74942340574238, 1.04392013153161e-166*log(2))

(-58.062062016304544, 2.20341707133417e-103*log(2))

(-23.135064085223007, 1.29677046056195e-32*log(2))

(-103.61585308729765, 9.50494882170421e-210*log(2))

(-0.015151205052940776, 0.693294755952549*log(2))

(-60.03301039073214, 9.98063074377722e-108*log(2))

(-65.9536307114313, 6.08294696811997e-121*log(2))

(-67.9294386091676, 2.09609502834855e-125*log(2))

(-56.092602232824966, 4.51456547604159e-99*log(2))

(-69.90624345428692, 6.78258070206504e-130*log(2))

(-79.80299666413121, 9.98074845885724e-153*log(2))

(-38.46566852755679, 5.63105728885574e-62*log(2))

(-21.27444198485439, 2.62030569849217e-29*log(2))

(-17.634316438266957, 4.70294591949102e-23*log(2))

(-14.181939064389356, 1.98726241289013e-17*log(2))

(-99.64260358597772, 4.72631914411261e-200*log(2))

(-25.014465777603764, 5.09820783795315e-36*log(2))

(-34.58646657464338, 3.06572061402714e-54*log(2))

(-30.731028950600496, 9.69053245605285e-47*log(2))

(-75.841973969979, 1.60533420968439e-143*log(2))

(-101.62904607121233, 6.84119934871485e-205*log(2))

(-97.65654380487254, 3.13148131124773e-195*log(2))

(-36.523531088104484, 4.42718621404162e-58*log(2))

(-87.73272153998387, 2.06640187236532e-171*log(2))

(-15.875445582052393, 3.79990920394035e-20*log(2))

(-77.82213153490427, 4.11304149710332e-148*log(2))

(-89.71654418968933, 3.89932605218455e-176*log(2))

(-19.438147790080837, 4.07981184938438e-26*log(2))

(-73.86257127291704, 5.92530033156056e-139*log(2))

(-91.70086300696663, 7.02226502770943e-181*log(2))

(-54.12476952058092, 8.55964770359e-95*log(2))

(-48.232725553681966, 3.54560109684878e-82*log(2))

(-32.65529342507171, 1.85371929615524e-50*log(2))

(-63.978897358608194, 1.65430630427161e-116*log(2))

(-95.67088622181049, 1.98803627006875e-190*log(2))

(-44.31641069242214, 5.81339466344838e-74*log(2))

(-52.158721364604595, 1.49711298374498e-90*log(2))

(-46.27322382515414, 4.76390839068697e-78*log(2))

(-42.36261192387418, 6.41161178684157e-70*log(2))

(-62.00532501950452, 4.20696222807405e-112*log(2))

(-71.88397537800067, 2.06490442513619e-134*log(2))

(-40.412212007351044, 6.35661658711601e-66*log(2))

(-12.590057506603054, 5.92441291136917e-15*log(2))

(-50.19463776177521, 2.4073265970624e-86*log(2))

(-26.90871895747249, 1.63102209966622e-39*log(2))

(-83.7666805001943, 5.02154683974981e-162*log(2))

(-81.78452616403935, 2.29715545672821e-157*log(2))

(-28.81495599275953, 4.32954475058933e-43*log(2))

(-93.68565177849987, 1.20820665742027e-185*log(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:
La función no tiene puntos mínimos
Puntos máximos de la función:
$$x_{49} = -0.0151512050529408$$
Decrece en los intervalos
$$\left(-\infty, -0.0151512050529408\right]$$
Crece en los intervalos
$$\left[-0.0151512050529408, \infty\right)$$