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$$- \operatorname{sign}{\left(x - 2 \right)} + \operatorname{sign}{\left(x + 1 \right)} = 0$$
Resolvermos esta ecuaciónRaíces de esta ecuación
$$x_{1} = 90$$
$$x_{2} = 18$$
$$x_{3} = 78$$
$$x_{4} = 50$$
$$x_{5} = 70$$
$$x_{6} = 30$$
$$x_{7} = -4$$
$$x_{8} = 24$$
$$x_{9} = 94$$
$$x_{10} = -100$$
$$x_{11} = -56$$
$$x_{12} = -6$$
$$x_{13} = 38$$
$$x_{14} = 46$$
$$x_{15} = -36$$
$$x_{16} = 6$$
$$x_{17} = 66$$
$$x_{18} = 82$$
$$x_{19} = -60$$
$$x_{20} = -90$$
$$x_{21} = 34$$
$$x_{22} = -88$$
$$x_{23} = -98$$
$$x_{24} = -44$$
$$x_{25} = -74$$
$$x_{26} = 84$$
$$x_{27} = 36$$
$$x_{28} = 72$$
$$x_{29} = 10$$
$$x_{30} = 48$$
$$x_{31} = -14$$
$$x_{32} = 80$$
$$x_{33} = -78$$
$$x_{34} = -62$$
$$x_{35} = -34$$
$$x_{36} = -46$$
$$x_{37} = -8$$
$$x_{38} = 42$$
$$x_{39} = 56$$
$$x_{40} = -24$$
$$x_{41} = 2.25$$
$$x_{42} = -16$$
$$x_{43} = -42$$
$$x_{44} = 64$$
$$x_{45} = 12$$
$$x_{46} = -50$$
$$x_{47} = 4$$
$$x_{48} = 28$$
$$x_{49} = 22$$
$$x_{50} = 16$$
$$x_{51} = 92$$
$$x_{52} = -40$$
$$x_{53} = -86$$
$$x_{54} = -84$$
$$x_{55} = -70$$
$$x_{56} = -68$$
$$x_{57} = 96$$
$$x_{58} = 74$$
$$x_{59} = -76$$
$$x_{60} = -82$$
$$x_{61} = 76$$
$$x_{62} = -96$$
$$x_{63} = -26$$
$$x_{64} = -38$$
$$x_{65} = -58$$
$$x_{66} = 86$$
$$x_{67} = 26$$
$$x_{68} = -52$$
$$x_{69} = -48$$
$$x_{70} = 52$$
$$x_{71} = -18$$
$$x_{72} = 60$$
$$x_{73} = 100$$
$$x_{74} = 88$$
$$x_{75} = -10$$
$$x_{76} = -20$$
$$x_{77} = -66$$
$$x_{78} = 40$$
$$x_{79} = -94$$
$$x_{80} = -12$$
$$x_{81} = -72$$
$$x_{82} = 54$$
$$x_{83} = -22$$
$$x_{84} = -30$$
$$x_{85} = 20$$
$$x_{86} = 14$$
$$x_{87} = 32$$
$$x_{88} = -32$$
$$x_{89} = 44$$
$$x_{90} = 62$$
$$x_{91} = -80$$
$$x_{92} = -28$$
$$x_{93} = -54$$
$$x_{94} = -64$$
$$x_{95} = 68$$
$$x_{96} = 58$$
$$x_{97} = -92$$
$$x_{98} = 98$$
$$x_{99} = -2$$
$$x_{100} = 8$$
Signos de extremos en los puntos:
(90, 3)
(18, 3)
(78, 3)
(50, 3)
(70, 3)
(30, 3)
(-4, -3)
(24, 3)
(94, 3)
(-100, -3)
(-56, -3)
(-6, -3)
(38, 3)
(46, 3)
(-36, -3)
(6, 3)
(66, 3)
(82, 3)
(-60, -3)
(-90, -3)
(34, 3)
(-88, -3)
(-98, -3)
(-44, -3)
(-74, -3)
(84, 3)
(36, 3)
(72, 3)
(10, 3)
(48, 3)
(-14, -3)
(80, 3)
(-78, -3)
(-62, -3)
(-34, -3)
(-46, -3)
(-8, -3)
(42, 3)
(56, 3)
(-24, -3)
(2.25, 3)
(-16, -3)
(-42, -3)
(64, 3)
(12, 3)
(-50, -3)
(4, 3)
(28, 3)
(22, 3)
(16, 3)
(92, 3)
(-40, -3)
(-86, -3)
(-84, -3)
(-70, -3)
(-68, -3)
(96, 3)
(74, 3)
(-76, -3)
(-82, -3)
(76, 3)
(-96, -3)
(-26, -3)
(-38, -3)
(-58, -3)
(86, 3)
(26, 3)
(-52, -3)
(-48, -3)
(52, 3)
(-18, -3)
(60, 3)
(100, 3)
(88, 3)
(-10, -3)
(-20, -3)
(-66, -3)
(40, 3)
(-94, -3)
(-12, -3)
(-72, -3)
(54, 3)
(-22, -3)
(-30, -3)
(20, 3)
(14, 3)
(32, 3)
(-32, -3)
(44, 3)
(62, 3)
(-80, -3)
(-28, -3)
(-54, -3)
(-64, -3)
(68, 3)
(58, 3)
(-92, -3)
(98, 3)
(-2, -3)
(8, 3)
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