f(x)=3x^3-7x^2-2.若f(X)可整理成f(x)=a(x-1)^3+b(x-1)^2+c(x-1)+d.求a.b.c.d的值.求f(0.99)的值.

f(x)=3x^3-7x^2-2.
若f(X)可整理成f(x)=a(x-1)^3+b(x-1)^2+c(x-1)+d
f(x)=ax^3-3ax^2+3ax-a+bx^2-2bx+b+cx-c+d
f(x)=ax^3-(3a-b)x^2+(3a-2b+c)x-a+b-c+d
3x^3-7x^2-2=ax^3-(3a-b)x^2+(3a-2b+c)x-a+b-c+d
a=3 3a-b=7 (3a-2b+c)=0 -a+b-c+d=-2
解得a=3 b=2 c=-5 d=-6
f(x)=a(x-1)^3+b(x-1)^2+c(x-1)+d
f(0.99)=3*(0.99-1)^3+2*(0.99-1)^2+（-5）*(0.99-1)-6
f(0.99)=-3*10^(-6)+2*10^(-4)-0.05-6
f(0.99)=5.950197不明为何ax^3-3ax^2+3ax-a=a(x-1)^3a(x-1)^3=a(x^3-3x^2+3x-1)=ax^3-3ax^2+3ax-a