Question: Show that if \(R\left( x \right)=6x\) and \(C\left( x \right)=x\left( {{\left( x-3 \right)}^{2}}+6 \right)\) are your revenue and cost functions, then your operation will never be profitable, and the best you can do is break even. (Hint: make a sign chart for the marginal profit and find the maximum value of R - C.)