На фото все решил, посмотри
1)0,008x³-0,6x²y+15xy²-125y³
2)27a³-16,2a²b+3,24ab²-0,216b³
3)0,001m³-0,12m²n+4,8mn²-64n³
4)0,125a³+0,12a²b+0,0384ab²+0,004096
1)a³+6a²b+12ab²+8b³
2)x³-9x²y+27xy²-27y³
3)8m³-36m²n+54mn²-27n³
Касательные параллельны оси абсцисс в точках экстремумов.
1) y' = 12x^3 - 84x^2 - 12x + 84 = 12(x-7)(x^2 - 1) = 12(x-7)(x-1)(x+1) = 0
x1 = -1; y(-1) = 3 + 28 - 6 - 84 + 1 = -58
x2 = 1; y(1) = 3 - 28 - 6 + 84 + 1 = 54
x3 = 7; y(7) = 3*2401 - 28*343 - 6*49 + 84*7 + 1 = -2106
2) y' = -2sin 2x + 5sin x = -4sin x*cos x + 5sin x = sin x*(5 - 4cos x) = 0
sin x = 0; x1 = 2pi*k; y(x1) = cos(4pi*k) - 5cos(2pi*k) = 1 - 5*1 = -4
x2 = pi + 2pi*k; y(x2) = cos(2pi+4pi*k) - 5(pi+2pi*k) = 1 - 5(-1) = 6
5 - 4cos x = 0; cos x = 5/4 > 1 - решений нет.
3) y' = (x - 4)^3 + x*3(x - 4)^2 = (x - 4)^2*(x - 4 + 3x) = (x - 4)^2*(4x - 4) = 0
x1 = x2 = 4; y(4) = 0
x3 = 1; y(1) = 1*(1 - 4)^3 = 1(-3)^3 = -27