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$$- \frac{\operatorname{sign}{\left(x + 1 \right)}}{x + 1} + \frac{\left|{x + 1}\right|}{\left(x + 1\right)^{2}} = 0$$
Resolvermos esta ecuaciónRaíces de esta ecuación
$$x_{1} = 90$$
$$x_{2} = 18$$
$$x_{3} = 78$$
$$x_{4} = 50$$
$$x_{5} = 70$$
$$x_{6} = 30$$
$$x_{7} = -4$$
$$x_{8} = 24$$
$$x_{9} = 94$$
$$x_{10} = -100$$
$$x_{11} = -56$$
$$x_{12} = -6$$
$$x_{13} = 38$$
$$x_{14} = 46$$
$$x_{15} = 2$$
$$x_{16} = -36$$
$$x_{17} = 6$$
$$x_{18} = 66$$
$$x_{19} = 82$$
$$x_{20} = -60$$
$$x_{21} = -90$$
$$x_{22} = 34$$
$$x_{23} = -88$$
$$x_{24} = -98$$
$$x_{25} = -44$$
$$x_{26} = -74$$
$$x_{27} = 0$$
$$x_{28} = 84$$
$$x_{29} = 36$$
$$x_{30} = 72$$
$$x_{31} = 10$$
$$x_{32} = 48$$
$$x_{33} = -14$$
$$x_{34} = 80$$
$$x_{35} = -78$$
$$x_{36} = -62$$
$$x_{37} = -34$$
$$x_{38} = -46$$
$$x_{39} = -8$$
$$x_{40} = 42$$
$$x_{41} = 56$$
$$x_{42} = -24$$
$$x_{43} = -16$$
$$x_{44} = -42$$
$$x_{45} = 64$$
$$x_{46} = 12$$
$$x_{47} = -50$$
$$x_{48} = 4$$
$$x_{49} = 28$$
$$x_{50} = 22$$
$$x_{51} = 16$$
$$x_{52} = 92$$
$$x_{53} = -40$$
$$x_{54} = -86$$
$$x_{55} = -84$$
$$x_{56} = -70$$
$$x_{57} = -68$$
$$x_{58} = 96$$
$$x_{59} = 74$$
$$x_{60} = -76$$
$$x_{61} = -82$$
$$x_{62} = 76$$
$$x_{63} = -96$$
$$x_{64} = -26$$
$$x_{65} = -38$$
$$x_{66} = -58$$
$$x_{67} = 86$$
$$x_{68} = 26$$
$$x_{69} = -52$$
$$x_{70} = -48$$
$$x_{71} = 52$$
$$x_{72} = -18$$
$$x_{73} = 60$$
$$x_{74} = 100$$
$$x_{75} = 88$$
$$x_{76} = -10$$
$$x_{77} = -20$$
$$x_{78} = -66$$
$$x_{79} = 40$$
$$x_{80} = -94$$
$$x_{81} = -12$$
$$x_{82} = -72$$
$$x_{83} = 54$$
$$x_{84} = -22$$
$$x_{85} = -30$$
$$x_{86} = 20$$
$$x_{87} = 14$$
$$x_{88} = 32$$
$$x_{89} = -32$$
$$x_{90} = 44$$
$$x_{91} = 62$$
$$x_{92} = -80$$
$$x_{93} = -28$$
$$x_{94} = -54$$
$$x_{95} = -64$$
$$x_{96} = 68$$
$$x_{97} = 58$$
$$x_{98} = -92$$
$$x_{99} = 98$$
$$x_{100} = -2$$
$$x_{101} = 8$$
Signos de extremos en los puntos:
(90, 1)
(18, 1)
(78, 1)
(50, 1)
(70, 1)
(30, 1)
(-4, 3)
(24, 1)
(94, 1)
(-100, 3)
(-56, 3)
(-6, 3)
(38, 1)
(46, 1)
(2, 1)
(-36, 3)
(6, 1)
(66, 1)
(82, 1)
(-60, 3)
(-90, 3)
(34, 1)
(-88, 3)
(-98, 3)
(-44, 3)
(-74, 3)
(0, 1)
(84, 1)
(36, 1)
(72, 1)
(10, 1)
(48, 1)
(-14, 3)
(80, 1)
(-78, 3)
(-62, 3)
(-34, 3)
(-46, 3)
(-8, 3)
(42, 1)
(56, 1)
(-24, 3)
(-16, 3)
(-42, 3)
(64, 1)
(12, 1)
(-50, 3)
(4, 1)
(28, 1)
(22, 1)
(16, 1)
(92, 1)
(-40, 3)
(-86, 3)
(-84, 3)
(-70, 3)
(-68, 3)
(96, 1)
(74, 1)
(-76, 3)
(-82, 3)
(76, 1)
(-96, 3)
(-26, 3)
(-38, 3)
(-58, 3)
(86, 1)
(26, 1)
(-52, 3)
(-48, 3)
(52, 1)
(-18, 3)
(60, 1)
(100, 1)
(88, 1)
(-10, 3)
(-20, 3)
(-66, 3)
(40, 1)
(-94, 3)
(-12, 3)
(-72, 3)
(54, 1)
(-22, 3)
(-30, 3)
(20, 1)
(14, 1)
(32, 1)
(-32, 3)
(44, 1)
(62, 1)
(-80, 3)
(-28, 3)
(-54, 3)
(-64, 3)
(68, 1)
(58, 1)
(-92, 3)
(98, 1)
(-2, 3)
(8, 1)
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