f(x)=x³-1/2x²-2x+5,x∈[-1,2],f'(x)=3x^2-x-2=0,x=-2/3,x=1 f(-1)=(-1)³-1/2(-1)²+2+5=11/2; f(-2/3)=(-2/3)³-1/2(-2/3)²-2(-2/3)+5=147/27; f(1)=(1)³-1/2(1)²-2+5=7/2; f(2)=(2)³-1/2(2)²-2(2)+5=7;所以在区间[-1,2]最大值是7,因此m>7.