f(x)=X^3+ax^2+1、设f(x)在区间(-2/3,-1/3)是减函数,求a取值范围.

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f(x)=X^3+ax^2+1、设f(x)在区间(-2/3,-1/3)是减函数,求a取值范围.
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f(x)=X^3+ax^2+1、设f(x)在区间(-2/3,-1/3)是减函数,求a取值范围.
f(x)=X^3+ax^2+1、设f(x)在区间(-2/3,-1/3)是减函数,求a取值范围.

f(x)=X^3+ax^2+1、设f(x)在区间(-2/3,-1/3)是减函数,求a取值范围.
y'=3x²+2ax≤0在(-2/3,-1/3)恒成立
即 3x+2a≥0在(-2/3,-1/3)恒成立
3x+2a的最小值为-2+2a≥0
a≥1

f'(x)=3x²+2ax,因在(-2/3,-1/3)上递减,则f'(-2/3)≤0且f'(-1/3)≤0,解得:a≥1