f(x)≥0恒成立,则:
m≥-(1/2)x^4-(2/3)x³
设:g(x)=-(1/2)x^4-(2/3)x³
则:g'(x)=-2x³-2x²=-2x²(x+1)
即:函数g(x)在(-∞,-1)上递增,在(-1,+∞)上递减,
得:函数g(x)的最大值是g(-1)=-(1/2)+(2/3)=1/6
因:m≥g(x)的最大值,则:
m≥1/6
f(x)≥0恒成立,则:
m≥-(1/2)x^4-(2/3)x³
设:g(x)=-(1/2)x^4-(2/3)x³
则:g'(x)=-2x³-2x²=-2x²(x+1)
即:函数g(x)在(-∞,-1)上递增,在(-1,+∞)上递减,
得:函数g(x)的最大值是g(-1)=-(1/2)+(2/3)=1/6
因:m≥g(x)的最大值,则:
m≥1/6