已知函数f(x)=ax^3+bx^2-x+c(a,b,c属于R且a不等于0)⑴若b=1且f(x)在(2,+∞)上存在单调递减区间,求a的取值范围⑵若存在实数x1,x2(x1不等于x2)满足f(x1)=f(x2),是否存在实数a,b,c使f(x)在(x1+x2)/2处的切线斜率

Question

已知函数f(x)=ax^3+bx^2-x+c(a,b,c属于R且a不等于0)
⑴若b=1且f(x)在(2,+∞)上存在单调递减区间,求a的取值范围
⑵若存在实数x1,x2(x1不等于x2)满足f(x1)=f(x2),是否存在实数a,b,c使f(x)在(x1+x2)/2处的切线斜率为0,若存在,求出一组实数a,b,c否则说明理由.

Answer 1

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