Исследуйте функцию на возрастание и убывание, определите экстремумы функций f(x)=x^3/3+x^2/2-2x-1

Y`=x²+x-2=0 x1+x2=-1 u x1*x2=-2⇒x1=-2 u x2=1       +              -            + возр.    -2  убыв.    1      возр.             max            min y(-2)=-8/3+2+4-1=2 1/3 y(1)=1/3+1/2-2-1=-2 1/6

Рассмотрим сразу числитель: sin 10 cos 55 + sin 280 sin 55 = sin 10 cos 55 + sin (270 + 10) sin 55 = [формулы = sin 10 cos 55 + (-cos 10) sin 55 = [sin (a-b) = sin a cos b - sin b cos a] = sin (10 - 55) = sin (-45) = - sin 45 = -√2/2 знаменатель: sin 10 cos 110 + sin 260 cos 200 = sin 10 cos (90 + 20) + sin (270 - 10) cos (180 +20) = sin 10 (-sin 20) + (-cos 10) (-cos 20) = cos 10 cos 20 - sin 20 sin 10 = [cos(a+b) = cos a cos b - sin a sin b] = cos (10+20) = cos 30 =  √3/2 все выражение: √6 * (-√2/2) / (√3/2) = -√6*√2*2 / (2√3) = -√2 *  √2 = -2

A^2-b^2=(a-b)(a+b)53^2 - 27^2 = (53 - 27)(53+27) = 26*80 = 208079^2 - 51^2 = (79-51)(79+51) = 28*130 = 364049^2 - 36^2= (49 - 36)(49+36) = 13*85 = 110558^2 - 42^2 = (58 - 42)(58+42) = 16* 100 = 1600120^2 - 55^2 = (120-55)(120+55) = 65* 1745=1137577^2 - 65^2= (77 - 65)(77+65) = 12*142 = 170435^2 - 14^2 = (35-14)(35+14) = 21*49=102942^2 - 22^2 = (42-22)(42+22) = 20*64=128015^2-6^2=(15-6)(15+6)= 9*21=18931^2-23^2= (31-23)(31+23)= 8*54=432 (a+b)^2=a^2+2ab+b^2 (40+1)^2 = 40^2 + 2*40*1 + 1^2 = 1600 + 80 + 1 = 1681(52 + 3)^2 = 52^2 + 2*52*3 + 3^2 = 2704 +312 +9 =  3025 (35 + 13)^2 = 35^2 + 2*35*12 + 13^2 = 1225 + 840 + 169 = 2234 (21 + 9)^2 = 21^2 + 2*21*9 + 9^2 = 441 + 378 + 81 = 900 (11 + 13)^2 = 11^2 + 2*11*13 + 13^2 = 121 + 286 + 169 = 576 (123 + 39)^2 = 123^2 + 2*123*39 + 39^2= 156129 + 9594 + 1521 = 167244 (55 + 19)^2 = 55^2 + 2*55*19 + 19^2 = 3025 + 2090 + 361 = 5476 (67 + 14)^2 = 67^2 + 2*67*14 + 14^2 = 4489 + 1876 + 196 = 6561 (98 + 3)^2 = 98^2 + 2*98*3 + 3^2 = 9604 + 588 + 9 = 10201 (83 + 19)^2 = 83^2 + 2*83*19 + 19^2 = 6889 + 3154 + 361 = 10404 (a-b)^2=a^2-2ab+b^2 (40-1)^2 = 40^2 - 2*40*1 + 1^2 = 1600 - 80 + 1 = 1521 (52 - 3)^2 = 52^2 - 2*52*3 + 3^2 = 2704 -312 +9 = 2401 (35 - 13)^2 = 35^2 - 2*35*12 + 13^2 = 1225 - 840 + 169 = 554 (21 - 9)^2 = 21^2 - 2*21*9 + 9^2 = 441 - 378 + 81 =  144(11 - 13)^2 = 11^2 - 2*11*13 + 13^2 = 121 - 286 + 169 = 4 (123 - 39)^2 = 123^2 - 2*123*39 + 39^2= 156129 - 9594 + 1521 = 148056 (55 - 19)^2 = 55^2 - 2*55*19 + 19^2 = 3025 - 2090 + 361 = 1296 (67 - 14)^2 = 67^2 - 2*67*14 + 14^2 = 4489 - 1876 + 196 = 2809 (98 -3)^2 = 98^2 - 2*98*3 + 3^2 = 9604 - 588 + 9 = 9025 (83 - 19)^2 = 83^2 - 2*83*19 + 19^2 = 6889 - 3154 + 361 = 4096 (a+b)^3=a^3+3a^2b+3ab^2+b^3(40 +1)^3 = 40^3 + 3*40^2*1 + 3*40*1^2 + 1^3 = 64000+4800+120+1 = 68921 (52+3)^3 = 52^3+3*52^2*3+3*52*3^2 + 3^3=140608+24336+1404+27=166375 (35+13)^3=35^3+3*35^2*13+3*35*13^2+13^3=42875+47775+17745+2197 = =109992 (21 +9)^3=21^3+3*21^2*9+3*21**9^2+9^3= 9261+11907+5103+729=27000 (11+13)^3= 11^3+3*11^2*13+3*11*13^2+13^3=1331+4719+5577+2197=13824 (12 +9)^3= 12^3+3*12^2*9+3*12*9^2+9^3= 1728+3888+2916+729=9261 (25 +8)^3= 25^3+3*25^2*8+3*25*8^2+8^3= 15625+15000+4800+512=35937 (6+7)^3 =6^3+3*6^2+7+3*6*7^2+7^3=216+756+882+343=2197 (9+13)^3 = 9^3+3*9^2*13+3*9*13^2+13^3=729+3159+4563+2197=10648 (8+11)^3 = 8^3+3*8^2*11+3*8*11^2+11^3=512+2112+2904+1331=6859 (a-b)^3=a^3-3a^2b+3ab^2-b^3 (40 -1)^3 = 40^3 - 3*40^2*1 + 3*40*1^2 - 1^3 = 64000-4800+120-1 =59319 (52-3)^3 = 52^3-3*52^2*3+3*52*3^2 - 3^3=140608-24336+1404-27=117649 (35-13)^3=35^3-3*35^2*13+3*35*13^2-13^3=42875-47775+17745-2197=10648 (21 -9)^3=21^3-3*21^2*9+3*21**9^2-9^3= 9261-11907+5103-729=1728 (11-13)^3= 11^3-3*11^2*13+3*11*13^2-13^3=1331-4719+5577-2197=-8 (12 -9)^3= 12^3-3*12^2*9+3*12*9^2-9^3= 1728-3888+2916-729=27 (25 -8)^3= 25^3-3*25^2*8+3*25*8^2-8^3= 15625-15000+4800-512=4913 (6-7)^3 =6^3-3*6^2+7+3*6*7^2-7^3=216-756+882-343=-1 (9-13)^3 = 9^3-3*9^2*13+3*9*13^2-13^3=729-3159+4563-2197=-64(8-11)^3 = 8^3-3*8^2*11+3*8*11^2-11^3=512-2112+2904-1331=-27 a^3+b^3=(a+b)(a^2-ab+b^2)3^3+ 5^3=(3+5)(3^2-3*5+5^2)= 8*(27-15+25)=8*37=296 9^3+4^3=(9+4)(9^2-9*4+4^2)=13*(81-36+16)=13*61=793 7^3+2^3=(7+3)(7^2-7*2+2^2)=10*(40-14+4)=10*30=300 6^3+8^3=(6+8)(6^2-6*8+8^2)=14*(36-48+64)=14*52=728 2^3+11^3=(2+11)(2^2-2*11+11^2)= 13*(4-22+121)=13*103=1339 12^3+7^3=(12+7)(12^2-12*7+7^2)=19*(144-84+49)=19*109=2071 15^3+11^3=(15+11)(15^2-15*11+11^2)=26*(225-165+121)=26*181=4706 13^3+12^3=(13+12)(13^2-13*12+12^2)=25*(169-156+144)=25*157=3925 14^3+16^3=(14+16)(14^2-14*16+16^2)= 30*(196-224+256)=30*228=6840 19^3+18^3=(19+18)(19^2-19*18+18^2)= 37*(361-342+324)=37*342=12691 a^3-b^3=(a-b)(a^2+ab+b^2)6^3- 5^3=(6-5)(6^2+6*5+5^2)= 1*(36+30+25)=1*91=91 9^3-4^3=(9-4)(9^2+9*4+4^2)=5*(81+36+16)=5*133=665 7^3-2^3=(7-3)(7^2+7*2+2^2)=7*(40+14+4)=7*58=406 6^3-3^3=(6-3)(6^2+6*3+3^2)=3*(36+18+9)=3*63=189 22^3-11^3=(22-11)(22^2+22*11+11^2)= 11*(484+242+121)=11*847=9317 12^3-7^3=(12-7)(12^2+12*7+7^2)=5*(144+84+49)=5*277=1385 15^3-11^3=(15-11)(15^2+15*11+11^2)=4*(225+165+121)=4*511=2044 13^3-9^3=(13-9)(13^2+13*9+9^2)=4*(169+117+81)=4*367=1468 16^3-14^3=(16-14)(16^2+16*14+14^2)= 2*(256+224+196)=2*676=1352 19^3-15^3=(19-15)(19^2+19*15+15^2)= 4*(361+285+225)=4*871=3484