Download In-class Workseet 4

Math 148
In-Class Worksheet #4
Spring 2015
Name:
1. Sketch a graph of f (x) = 2x2 − x4 using derivative tests to find the intervals where f is increasing
and decreasing, where f has relative extrema, and intervals of concavity.
2. At a certain factory, the cost of making a part is $30 per unit for labor and $10 per unit for materials.
Overhead for the factor is fixed at $30,000 per week. If more than 5000 units are produced each week,
and labor is $45 per unit for those units in excess of 5000, what level of production will minimize
average cost?
Math 148
In-Class Worksheet #4
Spring 2015
3. For a certain manufacturer, the cost function for a product is C(q) = 0.004q 3 + 20q + 5000. The
demand function for the product is p(q) = 450 − 4q. How many units should be sold in order to
maximize profit?
p
4. The demand equation for a certain product is given by q = 3000 − p2 . (Note that here we have q
in terms of p.) Find the point elasticity when p = $40. How does demand change when the price of
$40 is increased by 7%? What price will maximize revenue?