已经知a、b都为非负实数,且a+b=1,求M=a^3+b^3的最大值、最小值

M=(a+b)(a^2-ab+b^2)
=a^2-ab+b^2
=(a+b)^2-3ab
=1-3ab
1=a+b>=2√(ab)
所以0<=√(ab)<=1/2
0<=ab<=1/4
-3/4<=-3ab<=0
1-3/4<=1-3ab<=1+0
所以M最大值=1,最小值=1/4