1) f'(x)=-x²+8x-12
f'(x)=-4x(x³+1)-(-2x²+6)3x²/(x³+1)² = -4x⁴-4x+6x⁴-18x²/(x³+1)²= 2x⁴-4x-18x²/
/(x³+1)²
2)x=-1 x=-2 x=-3
- + - +
_______-3_______-2__________-1_______
Ответ:(-3;-∞)∪(-2;-1)
3)y=f(x0)+f'(x0)(x-x0)
f(x)=2x³-3x²+1 x0=3
f(x0)=2*27-3*9+1=54-27+1=28
f'(x)=6x²-6x
f'(x0)=6*9-18=54-18=36
y=28+36(x-3)=28+36x-108=36x-80
4)v=s' = 15t⁴-15t² = 15(t⁴-t²)=15*(81-9)=72*15=1080
a=v'=60t³-30t=30(2t³-t)=30*(2*27-3)=51*30=1530