設函數(shù)f(x)=ax^3+bx^2-3a^2x+1(a、b∈R)在x=x1,x=x2處取最值,且|x1-x2|=2,若a>0,求b 的取值范圍
設函數(shù)f(x)=ax^3+bx^2-3a^2x+1(a、b∈R)在x=x1,x=x2處取最值,且|x1-x2|=2,若a>0,求b 的取值范圍
設函數(shù)f(x)=ax^3+bx^2-3a^2x+1(a、b∈R)在x=x1,x=x2處取最值,且|x1-x2|=2,若a>0,求b
的取值范圍
設函數(shù)f(x)=ax^3+bx^2-3a^2x+1(a、b∈R)在x=x1,x=x2處取最值,且|x1-x2|=2,若a>0,求b
的取值范圍
數(shù)學人氣：572 ℃時間：2020-02-05 03:49:58
優(yōu)質(zhì)解答
分析：考察導數(shù)+不等式,f(x)=ax^3+bx^2-3a^2x+1求導得f'(x)=3ax^2+2bx-3a^2,判別式=4b^2+36a^3>0,又f(x)在x1,x2處取得最值.得f'(x)=0,有兩根.且x1+x2=-2b/(3a),x1x2=-a
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