依据上述结论,可知f(x)图像的对称中心为　　　　,f(1/(1" " 010))+f(2/(1" " 010))+...+f((1" " 009)/(1" " 010))=　　　　.

【解析】因为f(x)=x3-3/2x2+3x+3/4,

所以f'(x)=3x2-3x+3,f ″(x)=6x-1.

令f″(x)=0,则x=1/2.又因为f(1/2)=2,

所以对称中心为(1/2 "," 2).

设f(x)上任意一点P(x1,y1),因为f(x)关于(1/2 "," 2)对称,所以P关于(1/2 "," 2)对称的对称点P'(x2,y2)也在f(x)上,且x2=1-x1,y2=4-y1,

所以f(x1)+f(1-x1)=y1+4-y1=4,

f((x_1+1"-" x_1)/2)=f(1/2)=2,

所以f(1/(1" " 010))+f(2/(1" " 010))+...+f((1" " 009)/(1" " 010))=f(1/(1" " 010))+f((1" " 009)/(1" " 010))+...+f(504/(1" " 010))+f(506/(1" " 010))+f(505/(1" " 010))=4×504+2=2 016.

答案:(1/2 "," 2)　2 018

6.已知曲线y=(1-x)xn(n∈N*)在x=1/2处的切线为l,直线l在y轴上的截距为bn,则数列{bn}的通项公式为　　　　.

【解析】因为曲线y=(1-x)xn(n∈N*),

所以y'=-xn+n(1-x)xn-1=xn-1(n-nx-x),