Chapter 1.8, Problem 29E

Marginal Cost Analysis Consider the cost function $C\left(x\right)=6x^2+14x+18$

(thousand dollars).

What is the marginal cost at production level $x=5$?

Estimate the cost of raising the production level from $x=5$ to $x=5.25$.

Let $R\left(x\right)=-x^2+37x+38$ denote the revenue in thousands of dollars generated from the production of $\text{x}$

units. What is the breakeven point? (Recall that the breakeven point is when revenue is equal to cost.)

Compute and compare the marginal revenue and marginal cost at the breakeven point. Should the company increase production beyond the breakeven point? Justify your answer using marginals.