Para hallar los extremos hay que resolver la ecuación
$$\frac{d}{d z} f{\left(z \right)} = 0$$
(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
$$\frac{d}{d z} f{\left(z \right)} = $$
primera derivada$$\sin{\left(z \right)} \operatorname{sign}{\left(z \right)} + \cos{\left(z \right)} \left|{z}\right| = 0$$
Resolvermos esta ecuaciónRaíces de esta ecuación
$$z_{1} = 61.2773745335697$$
$$z_{2} = -36.1559664195367$$
$$z_{3} = 80.1230928148503$$
$$z_{4} = 33.0170010333572$$
$$z_{5} = -42.4350618814099$$
$$z_{6} = -17.3363779239834$$
$$z_{7} = 23.6042847729804$$
$$z_{8} = 67.5590428388084$$
$$z_{9} = -83.2642147040886$$
$$z_{10} = 42.4350618814099$$
$$z_{11} = -95.8290108090195$$
$$z_{12} = 20.469167402741$$
$$z_{13} = -11.085538406497$$
$$z_{14} = 64.4181717218392$$
$$z_{15} = -51.855560729152$$
$$z_{16} = -7.97866571241324$$
$$z_{17} = -20.469167402741$$
$$z_{18} = -86.4053708116885$$
$$z_{19} = -39.295350981473$$
$$z_{20} = -48.7152107175577$$
$$z_{21} = 54.9960525574964$$
$$z_{22} = -23.6042847729804$$
$$z_{23} = 86.4053708116885$$
$$z_{24} = -4.91318043943488$$
$$z_{25} = 29.8785865061074$$
$$z_{26} = 76.9820093304187$$
$$z_{27} = 2.02875783811043$$
$$z_{28} = -58.1366632448992$$
$$z_{29} = 11.085538406497$$
$$z_{30} = 14.2074367251912$$
$$z_{31} = 7.97866571241324$$
$$z_{32} = -80.1230928148503$$
$$z_{33} = -73.8409691490209$$
$$z_{34} = -54.9960525574964$$
$$z_{35} = 83.2642147040886$$
$$z_{36} = 58.1366632448992$$
$$z_{37} = -64.4181717218392$$
$$z_{38} = -45.57503179559$$
$$z_{39} = 26.7409160147873$$
$$z_{40} = -26.7409160147873$$
$$z_{41} = 17.3363779239834$$
$$z_{42} = -98.9702722883957$$
$$z_{43} = 89.5465575382492$$
$$z_{44} = 70.69997803861$$
$$z_{45} = 39.295350981473$$
$$z_{46} = -29.8785865061074$$
$$z_{47} = 45.57503179559$$
$$z_{48} = -67.5590428388084$$
$$z_{49} = 102.111554139654$$
$$z_{50} = 51.855560729152$$
$$z_{51} = 98.9702722883957$$
$$z_{52} = -89.5465575382492$$
$$z_{53} = 0$$
$$z_{54} = -70.69997803861$$
$$z_{55} = -76.9820093304187$$
$$z_{56} = -33.0170010333572$$
$$z_{57} = 73.8409691490209$$
$$z_{58} = 36.1559664195367$$
$$z_{59} = 48.7152107175577$$
$$z_{60} = -61.2773745335697$$
$$z_{61} = 95.8290108090195$$
$$z_{62} = -2.02875783811043$$
$$z_{63} = 4.91318043943488$$
$$z_{64} = -92.687771772017$$
$$z_{65} = -14.2074367251912$$
$$z_{66} = 92.687771772017$$
Signos de extremos en los puntos:
(61.277374533569656, -61.2692165444766)
(-36.15596641953672, 36.1421453722421)
(80.12309281485025, -80.1168531456592)
(33.017001033357246, 33.0018677308454)
(-42.43506188140989, 42.4232840772591)
(-17.33637792398336, 17.3076086078585)
(23.604284772980407, -23.5831306496334)
(67.5590428388084, -67.5516431209725)
(-83.26421470408864, -83.2582103729533)
(42.43506188140989, -42.4232840772591)
(-95.82901080901948, -95.8237936084657)
(20.46916740274095, 20.4447840582523)
(-11.085538406497022, 11.04070801593)
(64.41817172183916, 64.4104113393753)
(-51.85556072915197, -51.8459212502015)
(-7.978665712413241, -7.91672737158778)
(-20.46916740274095, -20.4447840582523)
(-86.40537081168854, 86.3995847156108)
(-39.295350981472986, -39.2826330068918)
(-48.715210717557724, 48.7049502253679)
(54.99605255749639, -54.9869632496976)
(-23.604284772980407, 23.5831306496334)
(86.40537081168854, -86.3995847156108)
(-4.913180439434884, 4.81446988971227)
(29.878586506107393, -29.8618661591868)
(76.98200933041872, 76.9755151282637)
(2.028757838110434, 1.81970574115965)
(-58.13666324489916, -58.1280647280857)
(11.085538406497022, -11.04070801593)
(14.207436725191188, 14.1723741137743)
(7.978665712413241, 7.91672737158778)
(-80.12309281485025, 80.1168531456592)
(-73.8409691490209, 73.8341987715416)
(-54.99605255749639, 54.9869632496976)
(83.26421470408864, 83.2582103729533)
(58.13666324489916, 58.1280647280857)
(-64.41817172183916, -64.4104113393753)
(-45.57503179559002, -45.5640648360268)
(26.74091601478731, 26.7222376646974)
(-26.74091601478731, -26.7222376646974)
(17.33637792398336, -17.3076086078585)
(-98.9702722883957, 98.9652206531187)
(89.54655753824919, 89.5409743728852)
(70.69997803861, 70.6929069615931)
(39.295350981472986, 39.2826330068918)
(-29.878586506107393, 29.8618661591868)
(45.57503179559002, 45.5640648360268)
(-67.5590428388084, 67.5516431209725)
(102.11155413965392, 102.106657886316)
(51.85556072915197, 51.8459212502015)
(98.9702722883957, -98.9652206531187)
(-89.54655753824919, -89.5409743728852)
(0, 0)
(-70.69997803861, -70.6929069615931)
(-76.98200933041872, -76.9755151282637)
(-33.017001033357246, -33.0018677308454)
(73.8409691490209, -73.8341987715416)
(36.15596641953672, -36.1421453722421)
(48.715210717557724, -48.7049502253679)
(-61.277374533569656, 61.2692165444766)
(95.82901080901948, 95.8237936084657)
(-2.028757838110434, -1.81970574115965)
(4.913180439434884, -4.81446988971227)
(-92.687771772017, 92.6823777880592)
(-14.207436725191188, -14.1723741137743)
(92.687771772017, -92.6823777880592)
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:
Puntos mínimos de la función:
$$z_{1} = 61.2773745335697$$
$$z_{2} = 80.1230928148503$$
$$z_{3} = 23.6042847729804$$
$$z_{4} = 67.5590428388084$$
$$z_{5} = -83.2642147040886$$
$$z_{6} = 42.4350618814099$$
$$z_{7} = -95.8290108090195$$
$$z_{8} = -51.855560729152$$
$$z_{9} = -7.97866571241324$$
$$z_{10} = -20.469167402741$$
$$z_{11} = -39.295350981473$$
$$z_{12} = 54.9960525574964$$
$$z_{13} = 86.4053708116885$$
$$z_{14} = 29.8785865061074$$
$$z_{15} = -58.1366632448992$$
$$z_{16} = 11.085538406497$$
$$z_{17} = -64.4181717218392$$
$$z_{18} = -45.57503179559$$
$$z_{19} = -26.7409160147873$$
$$z_{20} = 17.3363779239834$$
$$z_{21} = 98.9702722883957$$
$$z_{22} = -89.5465575382492$$
$$z_{23} = -70.69997803861$$
$$z_{24} = -76.9820093304187$$
$$z_{25} = -33.0170010333572$$
$$z_{26} = 73.8409691490209$$
$$z_{27} = 36.1559664195367$$
$$z_{28} = 48.7152107175577$$
$$z_{29} = -2.02875783811043$$
$$z_{30} = 4.91318043943488$$
$$z_{31} = -14.2074367251912$$
$$z_{32} = 92.687771772017$$
Puntos máximos de la función:
$$z_{32} = -36.1559664195367$$
$$z_{32} = 33.0170010333572$$
$$z_{32} = -42.4350618814099$$
$$z_{32} = -17.3363779239834$$
$$z_{32} = 20.469167402741$$
$$z_{32} = -11.085538406497$$
$$z_{32} = 64.4181717218392$$
$$z_{32} = -86.4053708116885$$
$$z_{32} = -48.7152107175577$$
$$z_{32} = -23.6042847729804$$
$$z_{32} = -4.91318043943488$$
$$z_{32} = 76.9820093304187$$
$$z_{32} = 2.02875783811043$$
$$z_{32} = 14.2074367251912$$
$$z_{32} = 7.97866571241324$$
$$z_{32} = -80.1230928148503$$
$$z_{32} = -73.8409691490209$$
$$z_{32} = -54.9960525574964$$
$$z_{32} = 83.2642147040886$$
$$z_{32} = 58.1366632448992$$
$$z_{32} = 26.7409160147873$$
$$z_{32} = -98.9702722883957$$
$$z_{32} = 89.5465575382492$$
$$z_{32} = 70.69997803861$$
$$z_{32} = 39.295350981473$$
$$z_{32} = -29.8785865061074$$
$$z_{32} = 45.57503179559$$
$$z_{32} = -67.5590428388084$$
$$z_{32} = 102.111554139654$$
$$z_{32} = 51.855560729152$$
$$z_{32} = -61.2773745335697$$
$$z_{32} = 95.8290108090195$$
$$z_{32} = -92.687771772017$$
Decrece en los intervalos
$$\left[98.9702722883957, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -95.8290108090195\right]$$