设X1 X2 (X1≠X2)是函数f(X)=ax^3;+bx^2-a^2x(a>0)的两个极值点题若｜X1｜+｜X2｜=2倍根号2,求b的最大值

设X1 X2 (X1≠X2)是函数f(X)=ax^3;+bx^2-a^2x(a>0)的两个极值点题若｜X1｜+｜X2｜=2倍根号2,求b的最大值
设X1 X2 (X1≠X2)是函数f(X)=ax^3;+bx^2-a^2x(a>0)的两个极值点题
若｜X1｜+｜X2｜=2倍根号2,求b的最大值

设X1 X2 (X1≠X2)是函数f(X)=ax^3;+bx^2-a^2x(a>0)的两个极值点题若｜X1｜+｜X2｜=2倍根号2,求b的最大值
f'(x)=3ax^2+2bx-a^2
x1+x2=-2b/3a x1*x2=-a/3
由上式可得
2b=-3a(x1+x2)=9x1x2(x1+x2)
∵|x1|+|x2|≥x1+x2
即max(x1+x2)=2√2
|x1|+|x2|≥2√(|x1||x2|)
=>2≥|x1||x2|≥x1x2
即max(x1x2)=2
max(b)=9[max(x1x2)*max(x1+x2)]/2=9*2*2√2/2=18√2