Math& 148 Business Calculus 5 Credits

On the other hand, when they produce and sell the 7501st widget it will cost an additional $325 and they will receive an extra$125 in revenue, but lose \$200 in profit. Recall from the Optimization section we discussed how we can use the second derivative to identity the absolute extrema even though all we really get from it is relative extrema. Let’s start things out with a couple of optimization problems.
The course meets twice weekly, with other work completed online. Now, we could get the average cost function, differentiate that and then find the critical point. However, this average cost function is fairly typical for average cost functions so let’s instead differentiate the general formula above using the quotient rule and see what we have. The cost to produce an additional item is called the marginal cost and as we’ve seen in the above example the marginal cost is approximated by the rate of change of the cost function, $$C\left( x \right)$$. So, we define the marginal cost function to be the derivative of the cost function or, $$C’\left( x \right)$$.