(1)在△OAB中=- ∴=t=t-t ∴=+=t+(1-t) (2)∵C1、C2,…,C9依次为线段AB的10等分点, ∴=+; =+; … =+; … =+; ∴++…+=(++…+)(+)=(+) 故λ= (3)设=x,则 f(P)=|-|+2|-|+3|-|+…+9|-|+10|-|, =||+2||+3||+…+9||+10|| =|x-1|+2|x-2|+3|x-3|+…+9|x-9|+10|x-10| 当x∈[k,k+1]时,k∈{0,1,2,3,4,5,6,7,8,9} f(x)=(x-1)+2(x-2)+…+k(x-k)+k(k+1-x)…+10(10-x) =x+2x+…+kx-(k+1)x-(k+2)x-…-10x-12-22-…-k2+(k+1)2+(k+2)2+…+102 =(k2+k-55)x-[12+22+…+k2-(k+1)2-(k+2)2-…-102] 当k∈{0,1,2,3,4,5,6}时,k2+k-55<0,函数为减函数 当k∈{7,8,9}时,k2+k-55>0,函数为增函数 故当k=7时,f(P)取最小值f(7)=1×6+2×5+3×4+4×3+5×2+6×1+7×0+8×1+9×2+10×3=112 |