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$$\frac{- \frac{\operatorname{sign}{\left(x - 2 \right)}}{2} + \frac{\operatorname{sign}{\left(x + 1 \right)}}{2}}{\sqrt{- \left|{x - 2}\right| + \left|{x + 1}\right|}} = 0$$
Resolvermos esta ecuaciónRaíces de esta ecuación
$$x_{1} = -56$$
$$x_{2} = -38$$
$$x_{3} = 86$$
$$x_{4} = 88$$
$$x_{5} = 8$$
$$x_{6} = -24$$
$$x_{7} = 12$$
$$x_{8} = -18$$
$$x_{9} = -50$$
$$x_{10} = 62$$
$$x_{11} = -62$$
$$x_{12} = 34$$
$$x_{13} = -100$$
$$x_{14} = -82$$
$$x_{15} = -54$$
$$x_{16} = -10$$
$$x_{17} = -98$$
$$x_{18} = 44$$
$$x_{19} = 24$$
$$x_{20} = -30$$
$$x_{21} = -40$$
$$x_{22} = -46$$
$$x_{23} = -2$$
$$x_{24} = 94$$
$$x_{25} = -96$$
$$x_{26} = 90$$
$$x_{27} = 72$$
$$x_{28} = 40$$
$$x_{29} = 30$$
$$x_{30} = 98$$
$$x_{31} = -58$$
$$x_{32} = -1.37880413799714$$
$$x_{33} = 2.25$$
$$x_{34} = 10$$
$$x_{35} = 56$$
$$x_{36} = -20$$
$$x_{37} = -4$$
$$x_{38} = 60$$
$$x_{39} = 82$$
$$x_{40} = -64$$
$$x_{41} = 22$$
$$x_{42} = 100$$
$$x_{43} = 64$$
$$x_{44} = -42$$
$$x_{45} = -28$$
$$x_{46} = 54$$
$$x_{47} = -92$$
$$x_{48} = -74$$
$$x_{49} = 70$$
$$x_{50} = 68$$
$$x_{51} = -88$$
$$x_{52} = -72$$
$$x_{53} = 84$$
$$x_{54} = -84$$
$$x_{55} = -8$$
$$x_{56} = 96$$
$$x_{57} = 48$$
$$x_{58} = 20$$
$$x_{59} = -68$$
$$x_{60} = -22$$
$$x_{61} = -80$$
$$x_{62} = 76$$
$$x_{63} = -76$$
$$x_{64} = -34$$
$$x_{65} = 26$$
$$x_{66} = -60$$
$$x_{67} = 66$$
$$x_{68} = -86$$
$$x_{69} = 18$$
$$x_{70} = 6$$
$$x_{71} = -70$$
$$x_{72} = 28$$
$$x_{73} = -48$$
$$x_{74} = 38$$
$$x_{75} = 4$$
$$x_{76} = 52$$
$$x_{77} = -12$$
$$x_{78} = -44$$
$$x_{79} = -94$$
$$x_{80} = -26$$
$$x_{81} = -16$$
$$x_{82} = 36$$
$$x_{83} = 80$$
$$x_{84} = 74$$
$$x_{85} = 32$$
$$x_{86} = -6$$
$$x_{87} = -90$$
$$x_{88} = -78$$
$$x_{89} = 16$$
$$x_{90} = -14$$
$$x_{91} = -66$$
$$x_{92} = 14$$
$$x_{93} = -32$$
$$x_{94} = -36$$
$$x_{95} = -52$$
$$x_{96} = 58$$
$$x_{97} = 78$$
$$x_{98} = 92$$
$$x_{99} = 46$$
$$x_{100} = 42$$
$$x_{101} = 50$$
Signos de extremos en los puntos:
(-56, 1.73205080756888*I)
(-38, 1.73205080756888*I)
(86, 1.73205080756888)
(88, 1.73205080756888)
(8, 1.73205080756888)
(-24, 1.73205080756888*I)
(12, 1.73205080756888)
(-18, 1.73205080756888*I)
(-50, 1.73205080756888*I)
(62, 1.73205080756888)
(-62, 1.73205080756888*I)
(34, 1.73205080756888)
(-100, 1.73205080756888*I)
(-82, 1.73205080756888*I)
(-54, 1.73205080756888*I)
(-10, 1.73205080756888*I)
(-98, 1.73205080756888*I)
(44, 1.73205080756888)
(24, 1.73205080756888)
(-30, 1.73205080756888*I)
(-40, 1.73205080756888*I)
(-46, 1.73205080756888*I)
(-2, 1.73205080756888*I)
(94, 1.73205080756888)
(-96, 1.73205080756888*I)
(90, 1.73205080756888)
(72, 1.73205080756888)
(40, 1.73205080756888)
(30, 1.73205080756888)
(98, 1.73205080756888)
(-58, 1.73205080756888*I)
(-1.3788041379971385, 1.73205080756888*I)
(2.25, 1.73205080756888)
(10, 1.73205080756888)
(56, 1.73205080756888)
(-20, 1.73205080756888*I)
(-4, 1.73205080756888*I)
(60, 1.73205080756888)
(82, 1.73205080756888)
(-64, 1.73205080756888*I)
(22, 1.73205080756888)
(100, 1.73205080756888)
(64, 1.73205080756888)
(-42, 1.73205080756888*I)
(-28, 1.73205080756888*I)
(54, 1.73205080756888)
(-92, 1.73205080756888*I)
(-74, 1.73205080756888*I)
(70, 1.73205080756888)
(68, 1.73205080756888)
(-88, 1.73205080756888*I)
(-72, 1.73205080756888*I)
(84, 1.73205080756888)
(-84, 1.73205080756888*I)
(-8, 1.73205080756888*I)
(96, 1.73205080756888)
(48, 1.73205080756888)
(20, 1.73205080756888)
(-68, 1.73205080756888*I)
(-22, 1.73205080756888*I)
(-80, 1.73205080756888*I)
(76, 1.73205080756888)
(-76, 1.73205080756888*I)
(-34, 1.73205080756888*I)
(26, 1.73205080756888)
(-60, 1.73205080756888*I)
(66, 1.73205080756888)
(-86, 1.73205080756888*I)
(18, 1.73205080756888)
(6, 1.73205080756888)
(-70, 1.73205080756888*I)
(28, 1.73205080756888)
(-48, 1.73205080756888*I)
(38, 1.73205080756888)
(4, 1.73205080756888)
(52, 1.73205080756888)
(-12, 1.73205080756888*I)
(-44, 1.73205080756888*I)
(-94, 1.73205080756888*I)
(-26, 1.73205080756888*I)
(-16, 1.73205080756888*I)
(36, 1.73205080756888)
(80, 1.73205080756888)
(74, 1.73205080756888)
(32, 1.73205080756888)
(-6, 1.73205080756888*I)
(-90, 1.73205080756888*I)
(-78, 1.73205080756888*I)
(16, 1.73205080756888)
(-14, 1.73205080756888*I)
(-66, 1.73205080756888*I)
(14, 1.73205080756888)
(-32, 1.73205080756888*I)
(-36, 1.73205080756888*I)
(-52, 1.73205080756888*I)
(58, 1.73205080756888)
(78, 1.73205080756888)
(92, 1.73205080756888)
(46, 1.73205080756888)
(42, 1.73205080756888)
(50, 1.73205080756888)
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
La función no tiene puntos máximos
No cambia el valor en todo el eje numérico