2010年普通高等学校招生全国统一考试福建卷文科数学第22题(本小题满分14分):已知函数f(x)=1/3x~3-x~2+ax+b的图像在点P(0,f(0))处的切线方程为y=3x-2.(Ⅰ)求实数a,b的值;(Ⅱ)设g(x)=f(x)+m/(x-1)是[2,+∞)上的增函数.(i)求实数m的最大值; Fujian Normal University, Vol 22 (This subheading out of 14 points): Known f (x) = 1 / 3x ~ 3-x ~ 2 + ax + b of the image at the point The tangent equation at P (0, f (0)) is y = 3x-2. (1) Find the values ​​of a and b; (2) Let g (x) = f (x) + m / 1) is an increasing function on [2, + ∞). (I) Find the maximum value of real number m;