假定某行业的长期总成本函数为三次方程: TC=a+bq+cq²+dq³。证明(用微积分)总成本

假定某行业的长期总成本函数为三次方程: TC=a+bq+cq²+dq³。证明（用微积分)总成本

函数至少在取a、b、c、d四个参数值时与U形平均成本曲线相一致。

Suppose the long - run total cost function for an industry is given by the cubic equation TC =a+bq+cq²+dq³. Show (using calculus ) that this total cost function is consistent with a U - shaped average cost curve for at least some values of a, b, c, d.