26.已知f(x)=x^3+3x^2-4x+1=a(x-1)^3+b(x-1)^2+c(x-1)+d,試求:(1)a+b+c+d之值(2)f(0.99)之值?

26.已知f(x)=x^3+3x^2－4x+1=a(x－1)^3+b(x－1)^2
+c(x－1)+d，試求：
(1)a+b+c+d之值
Sol
f(2)=8+12－8+1=a+b+c+d
a+b+c+d=13
(2)f(0.99)之值?
Set y=x-1
x^3+3x^2－4x+1=ay^3+by^2+cy+d
set x=1=>y=0
1+3－4+1=d=1
x^3+3x^2－4x+1=ay^3+by^2+cy+1
x^3+3x^2－4x=ay^3+by^2+cy
x^2+4x=ay^2+by+c
set x=1=>y=0
1+4=c=5
x^2+4x=ay^2+by+5
x^2+4x－5=ay^2+by
x+5=ay+b
set x=1=>y=0
1+5=b=6
a=1
f(x)=y^3+6y^2+5y+1
x=0.99=>y=－0.01
f(0.99)=(－0.01)^3+6*(－0.01)^2+5*(－0.01)+1
=－0.000001+0.0006－0.05+1
=0.950599