f'_(1)=lim(X →1左极限）
={f(x)-f(1)}/(x-1)
=lim(X →1左极限）
=(2x^3/3-2/3)/(x-1)
=lim(X →1左极限)lim2/3*(x^3-1)/(x-1)
=lim(X →1左极限）2/3*(x^2+x+1)
=2
f+'(1)=lim(X →1右极限）{f(x)-f(1)}/(x-1)
=lim(X →1右极限）（x^2-2/3)/(x-1)
=无穷
故该函数左导数存在,右导数不存在
因此选B